Methods and Systems to Identify Operational Reaction Pathways

ABSTRACT

The present invention provides a method for identifying an operational reaction pathway of a biosystem. The method includes (a) providing a set of systemic reaction pathways through a reaction network representing said biosystem; (b) providing a set of phenomenological reaction pathways of said biosystem, and (c) comparing said set of systemic reaction pathways with said set of phenomenological reaction pathways, wherein a pathway common to said sets is an operational reaction pathway of said biosystem. Also described is a method of refining a biosystem reaction network; a method of reconciling biosystem data sets; a method of determining the effect of a genetic polymorphism on whole cell function; and a method of diagnosing a genetic polymorphism-mediated pathology.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 10/367,248 filed Feb. 14, 2003, now issued as U.S. Pat. No.7,734,420; which claims the benefit under 35 USC §119(e) to U.S.application Ser. No. 60/419,023 filed Oct. 15, 2002, now expired. Thedisclosure of each of the prior applications is considered part of andis incorporated by reference in the disclosure of this application.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the construction of in silico modelorganisms and, more specifically, methods and systems specifyingoperational reaction pathways and for the generation of optimal insilico models of actual organisms.

1. Background Information

Therapeutic agents, including drugs and gene-based agents, are beingrapidly developed by the pharmaceutical industry with the goal ofpreventing or treating human disease. Dietary supplements, includingherbal products, vitamins and amino acids, are also being developed andmarketed by the nutraceutical industry. Additionally, efforts for fasterand more effective methods for biological fermentation and otherbioprocessing of food stuffs and industrial compounds has been underdevelopment. Faster and more efficient production of crops and otheragricultural products is also yet another area of intense development inthe food industry.

Because of the complexity of biochemical reaction networks in andbetween cells of an organism, even relatively minor perturbations causedby a therapeutic agent, change in a dietary component or environmentalor growth conditions, can affect hundreds of biochemical reactions. Suchchanges or perturbations can lead to both desirable and undesirableeffects in any therapeutic, industrial or agricultural process involvingliving cells. It would therefore be beneficial if a particular processcould predict the effects on a living system such as a cell or organismof such perturbations.

However, current approaches to therapeutic, industrial and agriculturaldevelopment for compounds and processes used therein do not take intoaccount the effect of perturbations on cellular behavior at the level ofaccuracy needed for efficient and economical production of products. Inorder to design effective methods of manipulating cellular activitiesfor the optimization of such processes or to achieve the optimalintended effect of an applied a compound, it would be helpful tounderstand cellular behavior from an integrated perspective.

However, cellular behaviors involve the simultaneous function andintegration of many interrelated genes, gene products and chemicalreactions. Because of this interconnectivity, it is difficult to predicta priori the effect of a change in a single gene or gene product, or theeffect of a drug or an environmental factor, on cellular behavior. Theability to accurately predict cellular behavior under differentconditions would be extremely valuable in many areas of medicine andindustry. For example, if it were possible to predict which geneproducts are suitable drug targets, it would considerably shorten thetime it takes to develop an effective antibiotic or anti-tumor agent.Likewise, if it were possible to predict the optimal fermentationconditions and genetic make-up of a microorganism for production of aparticular industrially important product, it would allow for rapid andcost-effective improvements in the performance of these microorganisms.

Thus, there exists a need for models and modeling methods that can beused to accurately simulate and effectively analyze the behavior ofcells and organisms under a variety of conditions. The present inventionsatisfies this need and provides related advantages as well.

SUMMARY OF THE INVENTION

The invention provides a method of identifying an operational reactionpathway of a biosystem. The method consists of: (a) providing a set ofsystemic reaction pathways through a reaction network representing saidbiosystem; (b) providing a set of phenomenological reaction pathways ofsaid biosystem, and (c) comparing said set of systemic reaction pathwayswith said set of phenomenological reaction pathways, wherein a pathwaycommon to said sets is an perational reaction pathway of said biosystem.

Also provided is a method of refining a biosystem reaction network. Themethod consists of: (a) providing a mathematical representation of abiosystem; (b) determining differences between observed behavior of abiosystem and in silico behavior of said mathematical representation ofsaid biosystem under similar conditions; (c) modifying a structure ofsaid mathematical representation of said biosystem; (d) determiningdifferences between said observed behavior of said biosystem and insilico behavior of said modified mathematical representation of saidbiosystem under similar conditions, and (e) repeating steps (d) and (e)until behavioral differences are minimized, wherein satisfaction of apredetermined accuracy criteria indicates an improvement in saidbiosystem reaction network.

Further provided is a method of reconciling biosystem data sets. Themethod consists of: (a) providing a first reaction network reconstructedfrom legacy data comprising a plurality of hierarchical reactioncategories; (b) providing a second reaction network obtained fromempirical data, and (c) determining a consistency measure between saidhierarchical reaction categories in said first reaction network andelements in said second reaction network, wherein a high degree of saidconsistency measure for said hierarchical reaction categories indicatesthe validity of said first reaction network or a subcomponent thereof.

A method of determining the effect of a genetic polymorphism on wholecell function is also provided. The method consists of: (a) generating areaction network representing a biosystem with a geneticpolymorphism-mediated pathology; (b) applying a biochemical orphysiological condition stressing a physiological state of said reactionnetwork, and (c) determining a sensitivity to said applied biochemicalor physiological condition in said stressed physiological state comparedto a reaction network representing a normal biosystem, wherein saidsensitivity is indicative of a phenotypic consequence of said geneticpolymorphism-mediated pathology.

The invention additionally provides a method of diagnosing a geneticpolymorphism-mediated pathology. The method consists of: (a) applying abiochemical or physiological condition stressing a physiological stateof a reaction network representing a biosystem with a geneticpolymorphism-mediated pathology, said applied biochemical orphysiological condition correlating with said geneticpolymorphism-mediated pathology, and (b) measuring one or morebiochemical or physiological indicators of said pathology within saidreaction network, wherein a change in said one or more biochemical orphysiological indicators in said stressed state compared to anunstressed physiological state indicates the presence of a geneticpolymorphism corresponding to said pathology.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic diagram for steps involved in determiningoperational pathways of a biochemical reaction network.

FIG. 2 a shows a schematic representation of systemic reaction pathwaysas one branch of a regulatory tree with the regulated genes shown on thehorizontal axis.

FIG. 2 b shows a process by which mathematical representations ofbiosystems can be improved in an iterative fashion using algorithmicapproaches and targeted experimentation.

FIG. 3 shows a phase plane for succinate for an in silico-generatedmetabolic flux profile of core metabolism in E. coli was prepared.

FIG. 4 shows phase I of a phase plane for a flux distribution matrixgenerated with the E. coli core metabolism using the oxygen andsuccinate input values show next to the figure.

FIG. 5 shows an Singular Value Decomposition (SVD) analysis on the fluxmatrix shown in FIG. 4.

FIG. 6 shows the contribution level of each condition, or point shown inphase I of the FIG. 4 phase plane, for various modes obtained from SVD.

FIG. 7 shows the contribution level of each condition, or point shown inphase I of the FIG. 4 phase plane, for various modes obtained from SVD.

FIG. 8 shows the reduced set of extreme pathways for succinate that ispresented in Table 2.

FIG. 9 shows a schematic diagram of flux balance analysis (FBA) andconvex analysis to identify extreme and operational pathways of theinvention.

FIG. 10 shows decomposed flux vectors using the modes obtained from SVDof P for the extreme pathways of the red blood cell (RBC) metabolicnetwork.

FIG. 11 shows a histogram of the first five modes of the SVD analysisshown in FIG. 10 under maximum (Max), moderate (Mid) and nominal state(no load) oxidative and energy loads.

FIG. 12 shows a schematic diagram for building large-scale in silicomodels of complex biological processes.

FIG. 13 shows the localization of single nucleotide polymorphismclusters found in clinically diagnosed glucose-6-phosphate dehydrogenase(G6PD) patients.

FIG. 14 shows the toleration of oxidative load between chronic and nonchronic hemolytic anemia states having G6PD SNPs.

FIG. 15 shows the characterization and toleration of energy loads forglycolytic states harboring different pyruvate kinase (PK) SNP variants.

FIG. 16 shows the reconciliation of legacy and empirical data sets forregulatory networks of yeast and E. coli.

FIG. 17 shows a schematic diagram of an algorithm for reconciliation ofdata sets and iterative improvement of a mathematical or in silicomodel.

FIG. 18 shows a skeleton network of core metabolism and regulation,together with a table containing relevant chemical reactions andregulatory rules which govern the transcriptional regulation.

FIG. 19 shows calculation of the expression of regulated genes in anactual organism and model system resulting from phase I of an iterativeprocess of the invention.

FIG. 20 shows computed flux distributions using flux balance analysis(FBA) for the aerobic growth without regulation using an in silico modelof the invention.

DETAILED DESCRIPTION OF THE INVENTION

The invention provides methods and systems for determining theinteraction, integration and coordination of a set of components of abiosystem. The invention can thus be used to rapidly and systematicallyspecify a reconstructed biochemical reaction network at the genome-scaleand to relate the activity of the components and their interaction to aspecific phenotype or physiological state. Understanding whichcomponents are operational under particular conditions allows forimproved methods of engineering desirable functions into living cells,fixing malfunctioning circuits, and controlling endogenous circuits bythe proper manipulation of the cells' environment. Furthermore, a rapidmethod for characterizing a biochemical network allows for thecharacterization of a virtually uncharacterized biosystem with a minimumof experimental effort.

The invention provides a method for determining the operational pathwaysof a biochemical reaction network. The invention method is practiced by(a) providing a biochemical reaction network, comprised of reactionswhich can be regulated; (b) providing a set of experimental data whichrepresent various physiological or pathological states of the biosystemunder given conditions; (c) determining a set of systemic pathways whichdefine the biosystem in whole or in part; (d) determining a set ofphenomenological reaction pathways which describe the experimentalstates of the biosystem ; and (e) determining the operational pathwayscommon to both the systemic and phenomenological pathways sets both atwhole-genome and biosystem subcomponent scale (FIG. 1).

As used herein, the term “reaction” is intended to mean a chemicalconversion that consumes a substrate or forms a product. A conversionincluded in the term can occur due to the activity of one or moreenzymes that are genetically encoded by an organism, or can occurspontaneously in a cell or organism. A conversion included in the termcan be, for example, a conversion of a substrate to a product, such asone due to nucleophilic or electrophilic addition, nucleophilic orelectrophilic substitution, elimination, reduction or oxidation. Aconversion included in the term can also be a change in location, suchas a change that occurs when a reactant is transported across a membraneor from one compartment to another. The substrate and product of areaction can be differentiated according to location in a particularcompartment, even though they are chemically the same. Thus, a reactionthat transports a chemically unchanged reactant from a first compartmentto a second compartment has as its substrate the reactant in the firstcompartment and as its product the reactant in the second compartment.The term “reaction” also includes a conversion that changes amacromolecule from a first conformation, or substrate conformation, to asecond conformation, or product conformation. Such conformationalchanges can be due, for example, to transduction of energy due tobinding a ligand such as a hormone or receptor, or from a physicalstimulus such as absorption of light. It will be understood that whenused in reference to an in silico biochemical reaction network, a“reaction” is intended to be a representation of a conversion asdescribed above.

As used herein, the term “reactant” is intended to mean a chemical thatis a substrate or a product of a reaction. The term can includesubstrates or products of reactions catalyzed by one or more enzymesencoded by an organism's genome, reactions occurring in an organism thatare catalyzed by one or more non-genetically encoded catalysts, orreactions that occur spontaneously in a cell or organism. Metabolitesare understood to be reactants within the meaning of the term. It willbe understood that when used in the context of an in silico model ordata structure, a reactant is understood to be a representation ofchemical that is a substrate or product of a reaction.

As used herein the term “substrate” is intended to mean a reactant thatcan be converted to one or more products by a reaction. The term caninclude, for example, a reactant that is to be chemically changed due tonucleophilic or electrophilic addition, nucleophilic or electrophilicsubstitution, elimination, reduction or oxidation or that is to changelocation such as by being transported across a membrane or to adifferent compartment. The term can include a macromolecule that changesconformation due to transduction of energy.

As used herein, the term “product” is intended to mean a reactant thatresults from a reaction with one or more substrates. The term caninclude, for example, a reactant that has been chemically changed due tonucleophilic or electrophilic addition, nucleophilic or electrophilicsubstitution, elimination, reduction or oxidation or that has changedlocation such as by being transported across a membrane or to adifferent compartment. The term can include a macromolecule that changesconformation due to transduction of energy.

As used herein, the term “regulatory reaction” is intended to mean achemical conversion or interaction that alters the activity of acatalyst. A chemical conversion or interaction can directly alter theactivity of a catalyst such as occurs when a catalyst ispost-translationally modified or can indirectly alter the activity of acatalyst such as occurs when a chemical conversion or binding eventleads to altered expression of the catalyst. Thus, transcriptional ortranslational regulatory pathways can indirectly alter a catalyst or anassociated reaction. Similarly, indirect regulatory reactions caninclude reactions that occur due to downstream components orparticipants in a regulatory reaction network. When used in reference toa data structure or in silico model, the term is intended to mean afirst reaction that is related to a second reaction by a function thatalters the flux through the second reaction by changing the value of aconstraint on the second reaction.

A regulatory reaction can further include information about inhibitoryor inducing effects of an active or inactive regulator on transcriptionof a gene. For example, a regulatory reaction may have one or moreregulators associated with it which effect transcription of a gene.

A regulatory reaction can further include information about theinteraction of regulators which influence gene expression. For example aregulatory reaction may have a combination of two or more regulatorsassociated with it which are dependent upon each other to effecttranscription of a gene.

A regulatory reaction can further include information in the form ofBoolean logic statements which indicates the interaction and dependencyof regulators for transcription of a particular gene. For example, aparticular gene may have a Boolean logic assigned to it which describesthe necessary regulators and regulatory interactions required forexpression of that gene.

As used herein, the term “regulator” refers to a substance whichregulates transcription, post-transcriptional modification or activityof one or more genes, proteins, mRNA transcripts. Such a regulator maybe a regulatory protein, small molecule and the like.

As used herein, the term “regulatory event” is intended to mean amodifier of the flux through a reaction that is independent of theamount of reactants available to the reaction. A modification includedin the term can be a change in the presence, absence, or amount of anenzyme that catalyzes a reaction. A modifier included in the term can bea regulatory reaction such as a signal transduction reaction or anenvironmental condition such as a change in pH, temperature, redoxpotential or time. It will be understood that when used in reference toan in silico model or data structure a regulatory event is intended tobe a representation of a modifier of the flux through a reaction that isindependent of the amount of reactants available to the reaction.

As used herein, the term “reaction network” refers to a representationof the functional interrelationships between a collection of reactionsand reaction components. Reaction components included in a reactionnetwork can be any component involved in a reaction, such as asubstrate, product, enzyme, cofactor, activator, inhibitor, transporter,and the like. Functional interrelationships include, for example, thosebetween a substrate and its product; those between a substrate orproduct and the enzyme that catalyzes the conversion from substrate toproduct; those between an enzyme and its cofactor, activator orinhibitor; those between a receptor and a ligand or other pairs ofmacromolecules that physically interact; those between a macromoleculeand its transporter; those between proteins involved in transcriptionalregulation and their DNA-binding sites in regulatory regions regulatingspecific target genes; and the like.

A reaction network can further include information regarding thestoichiometry of reactions within the network. For example, a reactioncomponent can have a stoichiometric coefficient assigned to it thatreflects the quantitative relationship between that component and othercomponents involved in the reaction.

A reaction network can further include information regarding thereversibility of reactions within the network. A reaction can bedescribed as occurring in either a reversible or irreversible direction.Reversible reactions can either be represented as one reaction thatoperates in both the forward and reverse direction or be decomposed intotwo irreversible reactions, one corresponding to the forward reactionand the other corresponding to the backward reaction.

A reaction network can include both intra-system reactions and exchangereactions. Intra-system reactions are the chemically and electricallybalanced interconversions of chemical species and transport processes,which serve to replenish or drain the relative amounts of certainreactants. Exchange reactions are those which constitute sources andsinks, allowing the passage of reactants into and out of a compartmentor across a hypothetical system boundary. These reactions represent thedemands placed on the biological system. As a matter of convention theexchange reactions are further classified into demand exchange andinput/output exchange reactions. Input/output exchange reactions areused to allow components to enter or exit the system. A demand exchangereaction is used to represent components that are required to beproduced by the cell for the purposes of creating a new cell, such asamino acids, nucleotides, phospholipids, and other biomass constituents,or metabolites that are to be produced for alternative purposes.

A reaction network can further include both metabolic and regulatoryreactions. Metabolic reactions can be represented by stoichiometry andreversibility while regulatory reactions can be represented by Booleanlogic statements which both depend on and effect the presence orabsence, activity or inactivity of metabolic or regulatory proteins.

A reaction network can be represented in any convenient manner. Forexample, a reaction network can be represented as a reaction map withinterrelationships between reactants indicated by arrows. Formathematical manipulation according to the methods of the invention, areaction network can conveniently be represented as a set of linearalgebraic equations or presented as a stoichiometric matrix. Astoichiometric matrix, S, can be provided, which is an m x n matrixwhere m corresponds to the number of reactants and n corresponds to thenumber of reactions in the network. Stoichiometric matrices and methodsfor their preparation and use are described, for example, in Schillinget al., Proc. Natl. Acad. Sci. USA 95:4193-4198 (1998). As a furtherexample, a reaction network can conveniently be represented as a set oflinear algebraic equations and Boolean logic equations. The Booleanlogic equations may be evaluated and lead to the removal or addition ofcertain reactions from the stoichiometric matrix, due to the inhibitoryor inducing effect of regulatory events. Such a representation isdescribed, for example, in Covert M W, Schilling C H, Palsson B. J TheorBiol. 213:73-88 (2001).

The invention methods can be practiced with reaction networks of eitherlow or high complexity, such as networks that include substantially allof the reactions that naturally occur for a particular biosystem. Thus,a reaction network can include, for example, at least about 10, 50, 100,150, 250, 400, 500, 750, 1000, 2500, 5000 or more reactions, which canrepresent, for example, at least about 5%, 10%, 20%, 30%, 50%, 60%, 75%,90%, 95% or 98% of the total number of naturally occurring reactions fora particular biosystem.

A reaction network represents reactions that participate in one or morebiosystems. As used herein, the term “biosystem” refers to an entireorganism or cell therefrom, or to a “biological process” that occurs in,to or by the organism or cell. Thus, a reaction network can representreactions that occur at the whole organismal, whole cell or subcellularlevel. Additionally, the reaction network may represent interactionsbetween different organisms or cells.

The term “organism” refers both to naturally occurring organisms and tonon-naturally occurring organisms, such as genetically modifiedorganisms. An organism can be a virus, a unicellular organism, or amulticellular organism, and can be either a eukaryote or a prokaryote.Further, an organism can be an animal, plant, protist, fungus orbacteria. Exemplary organisms include pathogens, and organisms thatproduce or can be made to produce commercially important products, suchas therapeutics, enzymes, nutraceuticals and other macromolecules.Examples of organisms include Arabidopsis thaliana, Bacillus subtilis,Bos taurus, Caenorhabditis elegans, Chlamydomonas reihardtii, Daniorerio, Dictyostelium discoideum, Drosophila melanogaster, Escherichiacoli, hepatitis C virus, Haemophilus influenzae, Helicobacter pylori,Homo sapiens, Mus musculus, Mycoplasma pneumoniae, Oryza sativa,Plasmodium falciparum, Pnemocystis carinii, Rattus norvegicus,Saccharomyces cerevisiae, Schizosaccharomyces pombe, Takifugu rubripes,Xenopus laevis, Zea mays, and the like.

A “biological process” of an organism or cell refers to a physiologicalfunction that requires a series of integrated reactions. A biologicalprocess can be, for example, cellular metabolism; cell motility; signaltransduction (including transduction of signals initiated by hormones,growth factors, hypoxia, cell-substrate interactions and cell-cellinteractions); cell cycle control; transcription; translation;degradation; sorting; repair; differentiation; development; apoptosis;and the like. Biological process are described, for example, in Stryer,L., Biochemistry, W.H. Freeman and Company, New York, 4th Edition(1995); Alberts et al., Molecular Biology of The Cell, GarlandPublishing, Inc., New York, 2nd Edition (1989); Kuby, Immunology, 3rdEdition, W.H. Freeman & Co., New York (1997); and Kornberg and Baker,DNA Replication, W.H. Freeman and Company, New York, 2nd Edition (1992).

In one embodiment, the biosystem includes the biological process ofcellular metabolism, and the reaction network representing thebiosystem, referred to as a “metabolic reaction network,” includescellular metabolic reactions. A basic review of cellular metabolism canbe found, for example, in Stryer, L., Biochemistry, W.H. Freeman andCompany, New York, 4th Edition (1995). Cellular metabolism can beusefully divided into central and peripheral metabolic reactions.Central metabolism includes reactions that belong to glycolysis, pentosephosphate pathway (PPP), tricarboxylic acid (TCA) cycle and respiration.Peripheral metabolism, which includes all metabolic reactions that arenot part of central metabolism, includes reactions involved in thebiosynthesis of an amino acid, degradation of an amino acid,biosynthesis of a purine, biosynthesis of a pyrimidine, biosynthesis ofa lipid, metabolism of a fatty acid, biosynthesis of a cofactor,metabolism of a cell wall component, transport of a metabolite ormetabolism of a carbon source, nitrogen source, phosphate source, oxygensource, sulfur source, hydrogen source or the like.

In another embodiment, the biosystem includes the biological process oftranscriptional regulation, and the reaction network representing thebiosystem, referred to as a “transcriptional regulatory reactionnetwork,” includes cellular transcriptional regulatory reactions. Abasic review of cellular transcriptional regulation can be found, forexample, in Alberts et al., Molecular Biology of The Cell, GarlandPublishing, Inc., New York, 2nd Edition (1989). Transcriptionalregulatory events may be grouped by the types of genes regulated, forexample those genes associated with metabolism, cell cycle, flagellarbiosynthesis and the like.

In another embodiment, the biosystem includes the biological processesof cellular metabolism and transcriptional regulation and the reactionnetwork representing the biosystem includes both metabolic andtranscriptional regulatory reactions.

A reaction network that includes substantially all of the reactions of awhole organism or cell, or substantially all of the reactions of aparticular biological process of an organism or cell, is referred to asa “genome-scale” reaction network. Genome-scale reaction networksrepresenting the metabolism of various organisms have been described,including E. coli (PCT publication WO 00/46405); H. pylori (Schilling etal., J. Bacteriol. 184:4582-4593 (2002)); and H. influenzae Edwards J.S. and Palsson B. O. J. Biol. Chem. 274:17410-6 (2001)).

For other biosystems, genome-scale reaction networks can be prepared bymethods known in the art. Generally, these methods involve firstgenerating a comprehensive list of reactions that are capable ofoccurring in the organism, cell or biosystem, and determining theirinterconnectivity. The list can include reactions determined from ananalysis of the annotated genome of the organism, supplemented asrequired from scientific literature and from experimental data. Alsoincluded can be transport reactions, biomass composition demands, growthassociated energy requirements, and the like.

The genome sequences of a large number of animals, plants, protists,fungi, bacteria and viruses have been completed or are in progress (see,for example, genome entries in The Institute for Genome Research (TIGR)database (www.tigr.org/tdb/) and in the NCBI Entrez Genome database(www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=Genome)). Other World WideWeb-based sources of annotated genome sequence information andreconstructed network information include EcoCyc, Metabolic pathwaysdatabase (MPW), Kyoto Encyclopedia of Genes and Genomes (KEGG), What isThere (WIT) and Biology Workbench.

For organisms whose genomes have not yet been sequenced, a variety ofmethods for obtaining the genomic sequence are known in the art. In mostlarge-scale genome sequencing methods, every step from isolating DNA,cloning or amplifying DNA, preparing sequencing reactions, andseparating and detecting labeled fragments to obtain sequence, isautomated (Meldrum, Genome Res. 10:1081-1092 (2000)). Most methods use acombination of sequencing methods, such as a combination of randomshotgun sequencing with a directed finishing phase. Other methods use awhole-genome shotgun approach, in which random fragments of totalgenomic DNA are subcloned directly, and high-throughput sequencing isused to provide redundant coverage of the genome. Another approach is tosequence each end of every BAC in a genome library, and match a finishedsequence to a BAC end sequence to select the next clone (Venter et al.,Science 280:1540-1542 (1998); Waterston et al, Science 282:53-54(1998)).

For a newly sequenced genome, the open reading frames (ORFs) or codingregions may be distinguished from the rest of the DNA sequence byvariety of methods. Determining the location of an ORF in a DNAsequence, its strand, and nucleotide composition may be conducted bysearching for gene signals (e.g., promoters, binding sites, start andstop codon, etc.) or by analzying gene content (e.g., codon preference,positional base frequency, etc.), or a combination of both methods.Algorithms and computational tools are available to determine the ORFsof an entire DNA sequence using these methods available throughinstitutes such as the University of Wisconsin Genetics Computer Groupand National Center for Biotechnology Information. Furthermore, othercomputational algorithms have been developed by which bacterial oreukaryotic genes may be identified by algorithmic methods such as hiddenMarkov models, which routinely find more than 99% of protein-codingregions and RNA genes (Pevzner, “Computational molecular biology: analgorithmic approach,” in Computational Molecular Biology. Cambridge,Mass.:MIT Press, xviii, p. 314 (2000); Baldi et al., “Bioinformatics:the machine learning approach,” in Adaptive Computation and MachineLearning. Cambridge, Mass,: MIT Press xviii, p. 351 (1998); Fraser etal., Nature 406:799-803 (2000)).

In order to assign function to the coding regions, newly identified ORFsare searched against databases containing genes and protein sequences ofknown function for sequence similarity. Several algorithms such as theBLAST and FASTA family of programs have been developed and are availablepublically by which the similarity of a functionally unknown ORF may bedetermined against functionally annotated genes. A major portion ofunidentified genes in a newly sequence organism can be assignedfunctionally with this procedure.

If the putative function of a gene is not established by gene or proteinsequence similarity, other techniques such as gene clustering byfunction or location may be used to assess the role of a gene in thenetwork. Gene products that participate in the same overall function canconstitute a pathway in the cell. “Missing links” in a pathwayconstructed from an initial sequence annotation suggests the existenceof genes that have not yet been identified. Searching the sequenceagainst other organisms provides clues about the possible nucleotidesequence of the missing genes, which in turn facilitates targetingfunctionality of the unassigned coding regions. Algorithms have beendeveloped that perform this procedure in various genome databases suchas KEGG and WIT. In addition, genes of the neighboring location may beclustered into operons that are regulated and function in a coordinatedfashion when the DNA sequence is compared to that of other organisms.From the annotated genetic information, together with biochemical andphysiological information, the interrelatedness of reactions andreaction components is determined and the reaction network is completed.

In addition to defining the ORFs or coding regions of the genome,regulatory regions can be defined by variety of methods. Regulatoryregions contain binding sites for transcriptional regulators andcomponents of the transcriptional machinery. These sites determine thespecificity of transcriptional regulation as the ability oftranscriptional regulators to regulate the gene controlled by theregulatory region. The methods to identify regulatory regions and sitesinclude comparing non-coding regions of closely related genomes toidentify highly conserved segments of the genome that may correspond toregulatory regions. Groups of non-coding regions of a genome can also besearched for commonly occurring sequence fragments to identify specificbinding site patterns in the genome. These groups can be defined forexample by similarity in biological function of the genes controlled bythe regulatory regions. In addition existing definitions of binding sitepatterns for specific transcriptional regulators stored in specificdatabases such as Saccharomyces Promoter Database (Zhu and Zhang,Bioinformatics 15:607-611 (1999)) or TRANSFAC (Wingender et al., Nucl.Acids Res. 29:281-283 (2001)) can be used to search the genome for newbinding sites for a regulator. Identifying regulatory sites for specifictranscription regulators allows establishing potential target genesregulated by these regulators and thus suggesting new regulatoryreactions to be added to the regulatory network.

As used herein, the term “reaction pathway” refers to a route through areaction network through which reaction components, regulatoryinformation or signaling molecules can potentially flow. It will beappreciated that the actual amount and/or rate of substrate to productconversion through a reaction pathway (also known as “flux”) is afunction of the physiological state of the biosystem underconsideration, and that reaction pathways (including operational,extreme and phenomenological reaction pathways as described below) aregenerally specified in connection with the physiological state of thebiosystem. The term “physiological state” is intended to refer to anyspecified internal and external parameters that affect, or are likely toaffect, flux through a biosystem. Parameters that can affect fluxinclude, for example, the actual or intended inputs to the biosystem(such as the carbon, nitrogen, phosphorus, sulfur or hydrogen source;the presence or amount of oxygen, nutrients, hormones, growth factors,inhibitors and the like); the actual or intended outputs of thebiological system (such as biomass components, secreted products and thelike) and environmental variables (such as temperature, pH and thelike). Other parameters that can affect flux include, for example, thestate of differentiation or transformation of the cell; cell age; itscontact with a substrate or with neighboring cells; the addition ordeletion of expressed genes; and the like.

As used herein, term “systemic reaction pathway” refers to a reactionpathway identified by an automated method applied to a suitablerepresentation of a reaction network. The method may involvemathematical or algorithmic operations to identify the reactionpathways, and it may include user definable parameters that influencethe identification of reaction pathways. The systemic reaction pathwaysneed not to be unique and they may only apply to a subset of thereaction network.

Methods of identifying systemic reaction pathways using convex analysishave been described in the art. Such methods include, for example,stoichiometric network analysis (SNA) (Clarke, Cell Biophys. 12:237-253(1988); elementary mode analysis (Schuster et al., Trends Biotech.17:53-60 (1999); and extreme pathway analysis (Schilling et al., J.Theor. Biol. 203:229-248 (2000); Schilling et al., Biotechnol. Bioeng.71:286-306 (2001)). The distinctions between these types of analysis aredescribed in Schilling et al. supra (2000).

In one embodiment, the systemic reaction pathway is an extreme pathway.The term “extreme pathway” refers to a systemically independent pathwaythat spans a convex, high-dimensional space that circumscribes allpotential steady state flux distributions achievable by a definedreaction network.

It will be understood that the steps needed to “provide” a set ofsystemic reaction pathways for use in the invention methods will dependon the amount and type of information already available regarding thebiosystem and reaction network. For certain biosystems and physiologicalstates, sets of extreme reaction pathways have been described in theart. For example, extreme pathways for a human red blood cell metabolicnetwork are described in Wiback et al., Biophys. J. 83:808-818 (2002).Extreme pathways for a H. influenzae metabolic network are described inSchilling et al., J. Theor. Biol. 203:249-283 (2000) and Papin et al.,J. Theor. Biol. 215:67-82 (2002). Extreme pathways for a H. pylorimetabolic network are described in Price et al., Genome Res. 12:760-769(2002).

Extreme reaction pathways can also be determined de novo, using methodsknown in the art (Schilling et al. supra (2000); Schilling et al. supra(2001)). Appropriate stoichiometric and thermodynamic constraints can beimposed on the intrasystem and exchange reactions in the reactionnetwork under steady-state conditions. Constraints can also imposed onthe input and output of reactants to and from the biosystem. Optionally,regulatory constraints can also be imposed (Covert et al., J. Theor.Biol. 213:73-88 (2001); Covert et al., J. Biol. Chem. 277:28058-28064(2002)). This results in a system of linear equalities and inequalitiesthat can be solved using convex analysis. The solution space correspondsgeometrically to a convex polyhedral cone in high-dimensional spaceemanating from the origin, which is referred to as the steady state“flux cone.” Within this flux cone lie all of the possible steady-statesolutions, and hence all the allowable flux distributions of thebiosystem. The extreme pathways correspond to vectors that define theedges of the flux cone.

In another embodiment, the systemic reaction pathway is one branch of aregulatory tree. The regulated genes of a biosystem may be depicted asshown in FIG. 2 a with the regulated genes shown on the horizontal axis.In a Boolean representation, each protein and each gene may beconsidered “on” or “off” (active or inactive, respectively). Thecombination of the activity state of all genes and proteins in abiosystem may be considered a “systemic regulatory pathway” or a“systemic signaling pathway”.

In another embodiment, the systemic reaction pathway is a set ofregulators and regulatory reactions influencing the activity of aregulated gene or the set of genes regulated by a regulator or a groupof regulators. These sets may be identified by analyzing theconnectivity of a regulatory network represented as a graph andidentifying nodes in the network connected to a particular node(regulator or regulated gene). The smallest possible set of such kind isone involving one regulatory reaction between a regulator and a targetgene.

As used herein, the term “phenomenological reaction pathway” refers to areaction pathway defined through analyzing experimental data to describethe state of the biosystem in whole or part. The data types that can beused to define phenomenological reaction pathways include but are notlimited to transcriptomic, proteomic, metabolomic, fluxomic,protein-protein interaction, and DNA-binding site occupancy data. Thedata analysis methods used to define the phenomenological pathways fromthe experimental data include but are not limited to systemsidentification, statistical, algorithmic, or signal processingtechniques.

Phenomenological information about the reactions and reactants of abiosystem can be determined by methods known in the art, and can beeither qualitative or quantitative. For example, phenomenologicalinformation can be obtained by determining transcription of genes,expression or interactions of proteins, production of metabolites orother reactants, or use of reactions in the biosystem. By analogy to theterm “genome,” such information, when obtained at the scale ofsubstantially the whole organism or cell, is called, respectively, the“transcriptome,” “proteome,” “metabolome” and “fluxome.”

Methods of determining gene expression at the transcriptome scale (alsoknown as “transcriptomics”) are known in the art and include, forexample, DNA microarray methods, which allow the simultaneous analysisof all transcripts simultaneously (Shena et al., Science 270:467-470(1995); DeRisi et al., Science 278:680-686 (1997)) and serial analysisof gene expression (SAGE) methods (Velculescu et al., Trends Genet.16:423-425 (2000)); Methods of determining protein expression (alsoknown as “proteomics”) are also known in the art. Expression proteomicmethods generally involve separation of proteins, such as bytwo-dimensional gel electrophoresis, followed by protein imaging usingradiolabels, dyes or stains. Separated proteins are then identifiedusing methods such as peptide mass fingerprinting by mass spectrometryand peptide-sequence tag, analysis by nano-electrospray (Blackstock etal., Trends Biotechnol. 17:121-127 (1999)).

Method for determining interactions between biological molecules in thecell at a large scale are also known in the art. Protein-proteininteraction information, which allows inferences as to a protein'sfunction, can be obtained, for example, using large-scale two-hybridanalysis to identify pairwise protein interactions (Fromont-Racine etal., Nat. Genet. 16:277-282 (1997). Indirect protein-DNA interactioninformation can be obtained using chromatin immunoprecipitation chip(ChIP-ChIP) methods, which allows the genome-scale identification ofgenomic binding sites of DNA-binding proteins and genomic targets oftranscription factors (Iyer et al., Nature 409:533-538 (2001)).

Methods of determining the complement of metabolites in a cell (alsoknown as “metabolomics”) are also known in the art and include, forexample, nuclear magnetic resonance (NMR) spectroscopy such as 13C-NMR;mass spectroscopy such as gas chromatography/time-of-flight massspectroscopy (GC/TOFMS); and liquid chromatography (Fiehn, Plant Mol.Biol. 48:155-171 (2002); Phelps et al., Curr. Opin. Biotech. 13:20-24(2002)).

Likewise, methods of measuring the fluxes through reaction pathways(also known as “fluxomics”) are known in the art, such as metabolic fluxratio analysis (METAFoR) (Sauer et al., J. Bacteriol. 181:6679-6688(1999)). METAFoR quantifies the relative abundance of intact carbonbonds in biomass constituents that originate from uniformly isotopicallylabeled precursor molecules, which reflects the metabolic pathways used.

By repeatedly varying the physiological state of the biosystem, eitherexperimentally or in silico, a series of phenomenological measurementsat different states can be obtained or predicted. These data can beorganized in vectorial form and represented in matrix or tabularformats. For example, a set of gene array expression data can beorganized as a matrix where each row is a gene, each column is anexperiment, and each value is an expression level or ratio. As anotherexample, a set of fluxome data can be organized as a matrix where eachrow is a reaction, each column is an experiment and each value is a fluxlevel or ratio. As a further example, a set of phenotypic data can beorganized as a matrix where each row is an experiment, each column is anenvironmental component (such as nutrients, waste products, or biomass)and each value is a rate of uptake, secretion, or growth.

The phenomenological information can be analyzed by various methodsknown in the art, such as methods of system identification, statisticaldata analysis, combinatorial algorithms, or signal processing todetermine a set of phenomenological reaction pathways.

Methods of system identification are known in the art and include, forexample, various types of clustering analysis methods (reviewed inSherlock et al., Curr. Opin. Immunol. 12:201-205 (2000)). Clusteringmethods can be applied to experimental data in matrix or tabular formatsto extract groups of genes that are co-expressed. These groups that caneither be disjoint or overlapping can be used as definitions ofphenomenological pathways. Alternatively, a data vector within eachcluster can be chosen to be a representative phenomenological pathwayfor that cluster—this vector could for example be the mean value of thedata points within the cluster also known as the centroid of thecluster.

Clustering analysis methods include, for example, hierarchicalclustering analysis (Eisen et al., Proc. Natl. Acad. Sci. USA95:14863-14868 (1998); Wen et al., Proc. Natl. Acad. Sci. USA 95:334-339(1998)), whereby single reactant profiles are successively joined toform nodes, which are then joined further. The process continues untilall individual profiles and nodes have been joined to form a singlehierarchical tree. Clustering analysis methods also include divisiveclustering analysis (Alon et al., Proc. Natl. Acad. Sci. USA96:6745-6750 (1999)), in which two vectors are initialized randomly, andeach reactant is assigned to one of the two vectors using a probabilityfunction. The vectors are iteratively recalculated to form the centroidsof the two clusters, and each cluster is successively split in the samemanner until each cluster consists of a single profile. Clusteringanalysis methods also include methods in which the data is partitionedinto reasonably homogeneous groups. Clustering methods that incorporatepartitioning include, for example, self-organizing maps (Kohenen, “SelfOrganizing Maps,” Berlin: Springer (1995); Tamayo et al., Proc. Natl.Acad. Sci. USA 96:2907-2912 (1999)) and k-means clustering (Everitt,“Cluster Analysis 122,” London: Heinemann (1974).

Another method of system identification is principal component analysisof the data, which is closely related to the singular valuedecomposition (SVD) of the data matrix (Holter et al., Proc. Natl. Acad.Sci. USA 97:8409-9414 (2000); Alter et al., Proc. Natl. Acad. Sci. USA97:10101-10106 (2000); Holter et al., Proc. Natl. Acad. Sci. USA98:1693-1698 (2001)). Principal component analysis is a statisticaltechnique for determining the key variables in a multidimensional dataset that explain the differences in the observations, and can be used tosimplify the analysis and visualization of multidimensional data sets.SVD is a linear transformation of data, such as gene expression data,from genes x arrays space to reduced diagonalized “eigengenes” x“eigenarrays” space, where the eigengenes (or eigenarrays) are uniqueorthonormal superpositions of the genes (or arrays). After normalizationand sorting of the data, the individual genes and arrays become groupedaccording to similar regulation and function, or similar physiologicalstate, respectively. Principal component and SVD analysis output a setof vectors in the data space (e.g., n dimensional where n is the numberof genes) ordered by how much of the variability in the data each vectoreach principal component or mode captures. These vectors can each beinterpreted as phenomenological pathways describing the major modes ofusage of the gene/protein complement of the organism under specificconditions that the experiments analyzed represent.

Software for various types of large-scale data analysis, includinghierarchical clustering, self-organizing maps, K-means clustering andprincipal component analysis, is known in the art or can be developedfor a particular application. Exemplary analysis software includes“XCluster” (see genome-www.stanford.edu/˜sherlock/cluster.html on theWorld Wide Web), “Cluster” software (see rana.lbl.gov/EisenSoftware.htmon the World Wide Web) and “Genesis” software (seegenome.tugraz.at/Software/Genesis/Description.html on the World WideWeb).

The skilled person can determine which method, or which combination ofmethods, is suitable to analyze phenomenological information todetermine a set of phenomenological reaction pathways.

As used herein, the term “operational reaction pathway” refers to asystemic reaction pathway of a biosystem that is feasible taking intoaccount the reactants present in, or fluxes through, the biosystem.Operational reaction pathways thus constitute a subset of systemicreaction pathways that are likely to actually exhibit flux in thebiosystem. The subset of systemic pathways that are consistent withphenomenological information about the biosystem are determined toidentify operational reaction pathways consistent with the reactantspresent or reaction fluxes through the biosystem.

Once a set of systemic reaction pathways and a set of phenomenologicalreaction pathways have been provided, the two sets are compared, andcommon pathways identified. As described above, the two sets of pathwayscan be represented in vectorial form, or in the form of groups of genesparticipating in the pathways, or in other convenient ways. There are anumber of mathematical methods known in the art by which two vectors ortwo groupings can be compared.

For example, the two sets of vectors can be compared using a number ofmeasures for pairwise similarity between vectors including: (1)Euclidean distance, which corresponds to the squared distance betweentwo points in space, or in this case two vectors, taking into accountboth the direction and the magnitude of the vectors (Hubbard J. H. andHubbard B. B. Vector Calculus, Linear Algebra, and Differential Forms,Prentice-Hall (1999)); (2) Pearson correlation coefficient, whichmeasures the angle between two vectors whose length is normalized toone, and is thus independent of the length of the vectors (Larsen R. J.and Marx M. L. An Introduction to Mathematical Statistics andApplications, Prentice Hall, New Jersey (1986)); or (3) Jackknifecorrelation coefficient, which is similar to Pearson correlationcoefficient, but is corrected for the effect of single outlierscomponents of the vectors to provide a more robust distance measure(Heyer et al., Genome Res. 9:1106-1115 (1999)). Other methods forcomparing vectors are known in the art.

Similarly, methods for comparing groupings of genes based on systemicand phenomenological definitions include: (1) the Rand index, whichmeasures the overlap between two different groupings of the same set ofgenes (Yeung K. Y et al. Bioinformatics 17:177 (2001)); and (2)correspondence analysis, which provides a two-dimensional graphicalrepresentation of the agreement between two groupings such that thesystemic and phenomenological pathways that are most similar to eachother are shown to be located closest to each other (Johnson R. A. andWichern D. W. Applied Multivariate Statistical Analysis, 5th Ed.,Prentice Hall, New Jersey (2002)).

The skilled person can determine which method, or which combination ofmethods, is suitable for comparing systemic reaction pathways andphenomenological reaction pathways to identify operational reactionpathways.

The invention also provides a method determining the effect of a geneticpolymorphism on whole cell function. The method consists of: (a)generating a reaction network representing a biosystem with a geneticpolymorphism-mediated pathology; (b) applying a biochemical orphysiological condition stressing a physiological state of the reactionnetwork, and (c) determining a sensitivity to the applied biochemical orphysiological condition in the stressed physiological state compared toa reaction network representing a normal biosystem, wherein thesensitivity is indicative of a phenotypic consequence of the geneticpolymorphism-mediated pathology. The biochemical or physiologicalcondition can be, for example, a change in flux load, pH, reactants, orproducts as well as system or subsystem changes such as those inoxidative or energy load.

Briefly, the above methods for analyzing physiological states of abiosystem, comparing them to systemic reaction pathways and determiningone or more operational reaction pathways can similarly be employed todetermine the effect of genetic polymorphisms on a biosystem orsubcomponent thereof. For example, phenomenological information used forcomparison with systemic reactions can be obtained from either actual orsimulated genetic mutations of enzymes or other polypeptides. Changes inactivity of the enzyme or polypeptide due to the mutation can beobtained from sources describing the defect or estimated based onavailable information or predictive computations using a variety ofmethods well known in the art. The activities that can be assessedinclude, for example, catalytic function of an enzyme or bindingactivity of a polypeptide such as a transcription regulator.

In silico models constituting a reaction network of a geneticpolymorphism can be constructed as described previously and the effectof the polymorphism can be assessed in context of the biosystem as awhole. Conditions that the reaction network are subjected to can bevaried and the effect of single or multiple, combined polymorphisms canbe determined on whole biosystem function or as the polymorphism relatesto subsystems thereof. For example, systemic pathways or operationalpathways can be calculated in the presence or absence of the geneticpolymorphism. Comparision of systemic pathways, operational pathways ora phenotypic manifestation between the two reaction networks can beperformed to determine the differences, if any, between the nativereaction network and the polymorphic counterpart. Such differences caninclude, for example, creation of a new systemic or operational pathway,omission of such a pathway and changes in the rate or magnitude of sucha pathway. The result of such changes between the normal and polymorphicstates also will reveal the consequential impact on biochemical orphysiological function or on phenotypic expression of the geneticpolymorphism.

Conditions that can be varied include, for example, any biochemical orphysiological component of the system. Such conditions can be eitherexternal to the biosystem including, for example, external environmentalgrowth conditions such as temperature, pH, carbon source and otherinput/output reactions which allow components to enter or exit thebiosystem. Alternatively, such biochemical or physiological conditionscan be internal to the biosystem. Specific examples of internalconditions include, for example, exchange reactions indicative ofsources and sinks allowing passage of reactants across a system orsubsystem boundary, intra-system reactions that replenish or drainreactants, and demand reactions which represent categories of componentsproduced by the cell. Biochemical or physiological conditions internalto the biosystem also can include changes in pH, utilization of carbonsources, availability of metabolites, cofactors, substrates andproducts. Other changed internal conditions can include, for example,alterations in system loads such as oxidative or energy load on itscorresponding subsystem. Various other biochemical or physiologicalconditions well known to those skilled in the art can similarly bevaried in the methods of the invention to obtain comparative reactionnetwork simulations for determining the effect of a genetic polymorphismon biosystem function.

Altering or changing a condition for each biosystem will generally besufficient for a comparison between a native and a counterpartpolymorhic biosystem. However, the effect can be enhanced when thebiochemical or physiological condition is applied to the native andpolymorphic biosystem at a magnitude sufficient to stress the biosystemor a correlative subsystem thereof. For example, where the activity of apolymorphic enzyme is altered only slightly compared to its nativecounterpart, the difference in activity may not substantially affectcellular function within an activity range tested. In part, aninsignificant impact on cellular function can be due to the productionof sufficient product to perform normal cellular activity regardless ofan activity deficiency. However, where the activity of the polymorphicenzyme is tested under stressed conditions, it can be unable to fulfillthe added cellular demand due to the additional work required of thesystem. Accordingly, under stressed conditions, a comparison of thenative reaction network functioning and that of the polymorphic reactionnetwork will more readily reveal those activity effects of thepolymorphic enzyme due to failure of product production under excessrequirements.

The term “stress” or “stressing” as used in reference to applying abiochemical or physiological condition is intended to mean placing abiosystem, reaction network or subsystem thereof under a state of strainor influence of extra effort. The stress can be mild or intense so longas it applies demands, loads or effort on the components extra to thatunder the normal or nominal state of the biosystem, reaction network orsubsystem thereof. Therefore, stressing a system state is intended toinclude imposing a condition that causes the system to exert additionaleffort toward achieving a goal. Specific examples of applying abiochemical or physiological condition to a biosystem that stresses aphysiological state is described further below in Example III.

Genetic polymorphisms can constitute, for example, single nucleotidepolymorphisms (SNPs) and well as multiple changes within a encoding generesulting in a polymorphic region within the gene or its polypeptidecoding region. Polymorphisms in gene or coding region structure canalter the expression levels of the harboring nucleic acid, activity ofthe encoded polypeptide or both. Polymorphisms well known to thoseskilled in the art of genetics and genomics include, for example,allelic variants of genes, SNPs and polymorphic regions of a referencednucleic acid. Specific examples, of genetic polymorphisms include thosevariations in coding sequence described in Example III forglucose-6-phosphate dehydrogenase (G6PD) and pyruvate kinase (PK).Numerous other genetic polymorphisms and their associated diseases aresimilarly well known to those skilled in the art.

Given the teachings and guidance provided herein, the methods of theinvention for determining the effect of a genetic polymorphism oncellular function can be used with any known or subsequently determinedgenetic polymorphism. Similarly, the linkage between the genetic defectand the pathology mediated also can be previously known or subsequentlydetermined. Moreover, and as described further below, it can be used todiagnose previously undetermined genetic polymorphisms that alter anactivity of an enzyme or polypeptide. However, by determining the effectof the defect in the context of a whole biosystem, a more accuratephenotype and assessment of the functional abilities of the biosystemcan be obtained. Accurate determination of phenotypic and functionalattributes of such complicated systems can be advantageously applied fora more meaningful treatment of the genetic polymorphism-mediateddisease.

Sensitivities of the polymorphic enzyme to the stressed condition can bemore or less pronounced depending on which polymorphisim is incorporatedinto the reaction system, the degree of polypeptide activity change dueto the polymorphism and the level of stress that is exerted on thesystem. Those skilled in the art will know or can determine, given theteachings and guidance provided herein, what sensitivities areindicative of a particular polymorphic enzyme or other polypeptide. Forexample, glucoso-6-phosphate dehydrogenase (G6PD) functions in theoxidative branch of the pentose pathway and is sensitive to changes inmaximum velocity (V_(max)) and cofactor binding affinity (K_(i-NADPH)).Enzymes with alterations in these activities result in changed inoxidative requirements which can be used as indicators of the metabolicstate for G6PD′s having altered activity. For example, one sensitiveindicator of the metabolic state of the biosystem is the NADPH/NADPratio. This ratio can be measured under stressed conditions and comparedbetween the polymorphic reaction network with that of the normal networkto determine the phenotypic and functional changes on the biosystem. Asdescribed further below in Example III, polymorphic enzymes havingalterations in these G6PD activities can be distinguished in the methodsof the invention as those mediating non-chronic and chronic hemolyticanemia.

Similarly, pyruvate kinase (PK) functions in glycolysis and is sensitiveto changes in V_(max) and the affinity for substrates such asphosphoenolpyruvate (K_(PEP)). Alterations in these activities result inchanges in ATP concentration, and 2,3 DPG concentration. Sensitiveindicators of V_(max) and K_(PEP) can include, for example, theconcentration of ATP when the biosystem is under maximum energy loads orstress compared to normal conditions. As with G6PD, polymorphic PKenzymes having alterations in these activities show that anemic patientshave a diminished ability to deviate from the normal homeostatic state.

For determining the effect on function, a reaction network specifyingthe activity of the polymorphic enzyme is constructed and the system isstressed as described above. Sensitivity to the stressed conditioncompared to that of the normal or native reaction network can then bedetermined using a variety of indicators. Those described above for G6PDand PK are exemplary indicators for enzyme activity. Those skilled inthe art will understand, given the teachings and guidance providedherein that other indicators of biochemical or physiological activity ofthe particular enzyme or polypeptide being assessed can be used in themethods of the invention. For example, essentially any measure ofsubstrate, product, cofactor, or other metabolite can be used as anindicator of polypeptide activity. Such indicators can be assesseddirectly or indirectly such as by measuring the products of downstreamreactions and the like. Moreover, ratios of such indicators or ofgeneral indicators of a particular biochemical or physiological statecan similarly be used. For example, ATP, and energy cofactors such asNADPH and NADP are general indicators of the oxidative state and energycharge, respectively, of a biosystem.

Changes in activity under stressed conditions of such biochemical orphysiological indicators will identify the change in function of thebiosystem due to the altered activity as well as show the phenotypicconsequences of the polymorphic enzyme. For example, the inability of abiosystem to respond to excess oxidative or energy requirements canshow, for example, that the polymorphic enzyme is unable to adequatelyproduce components within its assigned subsystem to handle the increasedwork requirements caused by the stress. A functional biosystem changecan correspond to, for example, altered demands and products that areproduced as well as changes in flux or pathways which compensate thedeficient enzyme activity. A phenotypic outcome can be, for example,inhibition of biosystem proliferation, decrease in biosystem mass oreven biosystem lysis and death.

The methods of the invention also can be used for diagnosis of a geneticpolymorphism-mediated pathology. The methods described above can be usedto generate a biosystem reaction network representing activities ofsuspected genetic polymorphism. The biosystem reaction network can bestressed as described above and the reaction network containing thesuspected polymorphic enzyme activity compared to that of a normalreaction network. A change in function or phenotype of the suspectedpolymorphic network compared to the normal will indicate that thegenetic alteration is linked to the enzyme deficiency. Those skilled inthe art will understand that a plurality of suspected enzyme defects canbe identified and linked to a particular disease given the teachings andguidance provided herein. For example, those skilled in the art can useactivity measurements from a suspected patient in the creation of aplurality of reaction networks. Comparison of the function or phenotypeof the networks harboring suspect activities with normal networks willidentify the differences in function or phenotype and whether any ofsuch identified differences are sufficient to result in a pathologicalcondition.

Therefore, the invention provides a method of diagnosing a geneticpolymorphism-mediated pathology. The method consists of: (a) applying abiochemical or physiological condition stressing a physiological stateof a reaction network representing a biosystem with a geneticpolymorphism-mediated pathology, the applied biochemical orphysiological condition correlating with the geneticpolymorphism-mediated pathology, and (b) measuring one or morebiochemical or physiological indicators of the pathology within thereaction network, wherein a change in the one or more biochemical orphysiological indicators in the stressed state compared to an unstressedphysiological state indicates the presence of a genetic polymorphismcorresponding to the pathology.

The invention further provides a method of reconciling biosystem datasets. The method consists of: (a) providing a first regulatory networkreconstructed from legacy data comprising a plurality of hierarchicalregulatory events; (b) providing a second regulatory network obtainedfrom empirical data, and (c) determining a consistency measure betweenthe hierarchical regulatory events in the first regulatory network andelements in the second regulatory network, wherein a high degree of theconsistency measure for the hierarchical regulatory events indicates thevalidity of the first regulatory network or a subcomponent thereof.

The method of the invention for reconciling data sets is useful fordetermining the accuracy of a biosystem model as well as for identifyingnew components, linkages, networks and subnetwork of a biosystem model.The model can be based on scientifically proven data, mathematicalinterpretations as well as on pure computational analysis or eventheoretical prediction. Regardless of the source of a biosystem model,the method for reconciling data sets compares the model or a data setrepresentation thereof to another source of data to identify theconsistency between one model or data set and that of the comparisonmodel or data set. The degree of consistency between the two models ordata sets thereof will show how accurate the initial model is to itscorresponding natural biosystem.

Data sets representing whole biosystems can be reconciled using themethods of the invention as well as any substructure thereof.Substructures can consist of subnetworks or modules of the biosystemreaction network. While the exact boundaries of subnetworks andboundaries can vary depending on the assessment criteria used, onefeature is that such substructures can be evaluated, analyzed oridentified as a unit in itself. Criteria for boundary determination caninclude, for example, functional attributes, structural attributes andgraphical or mathematical separateness, for example. Specific examplesof subnetworks or modules of a biosystem have been described above andbelow and are further shown in FIG. 16 and its associated Example IV.Other examples are well known to those skilled in the art and can beemployed in the methods of the invention given the teachings providedherein.

Data sets applicable for comparison can include a broad range ofdifferent types and sizes. For example, the data sets can contain alarge and complex number of diverse data elements or components of thereaction network. Alternatively, the data sets can be small andrelatively simple such as when comparing subnetworks or modules of thereaction network. Those skilled in the art will appreciate that the moreinclusive each data set for comparison is with respect to its systemcomponents, the more accurate and reliable will be the consistencymeasure. However, those skilled in the art will know, or can determine,a reliable means to compensate for inherent differences based on thecharacter of one or both of the initial data sets. Therefore, the methodof the invention can be used for reconciling data sets where the pair ofdata sets for comparison can be either large or small, or diverse orsimple, as well as for comparison where the data sets within the pairare either large or small, or diverse or simple with respect to eachother.

As used herein, the term “legacy” or “legacy data” is intended to referto known information or data such as that obtainable from literature,other reports, computational data, databases or a combination thereof.The information can be obtained from the public domain or previouslyknown by the user's own investigations. The term therefore is intendedto include secondary data that has received the benefit of scientificevaluation and considerations toward the system to which it pertains,the scientific authenticity or the theory which it promotes. Legacy datain essentially any obtainable form can be used in the methods of theinvention and can include, for example, literary, graphical, electronic,mathematical or computational forms as well as functional equivalentsand transformations thereof. Given the teachings and guidance providedherein, those skilled in the art will known how to use a particularformat either directly or following transformation into a useful formatfor representing a reaction network of the invention. A variety of suchuseful formats have been described above and below and others are wellknown to those skilled in the art.

As used herein, the term “empirical” or “empirical data” refers to databased on primary factual information, observation, or direct senseexperience. Empirical data is therefore intended to refer to raw data orprimary data that has not received the benefit of scientific evaluationand considerations toward the system to which it pertains, thescientific authenticity or the theory which it promotes. The term isintended to include, for example, data, data sets or equivalenttransformational forms thereof corresponding to gene expression data,protein activity data and the like. It can include, for example, large,high throughput datasets such as that obtainable by genomic, proteomic,transcriptomic, metabolic and fluxomic data acquisition as well as smalldata sets obtainable by a variety of research methods well known tothose skilled in the art. Other forms of primary data well known tothose skilled in the art can similarly be employed in the methods of theinvention.

Useful attributes of reconciling data sets include, for example, bothvalidation of known reaction network and subnetwork models as well asthe identification or discovery of new subnetworks or modules thereof.Validation of an existing model is useful in itself because itauthenticates previous scientific theories as well as subsequentdiscoveries based on the original model. Similarly, invalidation of anetwork model can be useful, for example, because it informs the userthat components, links or scientific premises may be omitted from thenetwork model as a whole. Moreover, reconciliation of data sets canidentify subnetworks or modules of the biosystem reaction network modelby showing differential validation of a particular subsystem or ofseveral subsystems within the whole. For example, discovery of newsubnetworks or identification of valid subnetworks within the whole canoccur when some, but not all, modules within the biosystem network arereconciled. Identifications are particularly striking where thesubnetwork or module thereof constitute relatively independent entitieswithin the biosystem reaction network or are relatively decoupled fromthe body of the biosystem network. Finally, information gained fromreconciliation of data sets and validation of whole networks,subnetworks or modules thereof can be used to refine the network orsubnetworks by altering the model determining whether the altered modelreconciles with the comparative data set.

Validation and discovery methods of the invention are applicable toessentially any form or format of the reaction network. For example,data sets can be reconciled where a reaction network is represented byan in silico model, a mathematical representation thereof, a statisticalrepresentation, computational representation, graphical representationor any of a variety of other formats well known to those skilled in theart.

Reconciliation of data sets allows for the validation of essentially anycausal relationships within the compared biosystem networks. Forexample, the method for reconciliation of data sets can be employed ondata sets specifying all types of reaction networks described herein.Therefore, the method is applicable to reaction networks correspondingto a metabolic reaction network, a regulatory reaction network, atranscriptional reaction network or a genome-scale reaction network, orany combination thereof. To perform the method of reconciliation, afirst reaction network can be provided that is reconstructed from legacydata. As described previously, the legacy data can be obtained from asecondary source that has assembled primary data into a working model ofthe biosystem network components. The first reaction network is comparedwith a second reaction network obtained from empirical data. Theempirical data can consist of, for example, any primary datarepresenting an activity or other attribute of the components within thebiosystem.

A comparison of data sets can be accomplished by, for example, anymethod known to those skilled in the art that provides a measure ofconsistency between the network representation and the empirical data.In one embodiment a consistency measure is determined between theempirical data and the legacy data, or the legacy-derived network modelby, for example, grouping the network components into hierarchicalorganization of reaction categories. The reaction categories are usefulfor determining consistency measurements between the data sets to bereconciled. The reaction categories can include, for example, reactantsand products, reaction fluxes, metabolic reactions, regulatory reactionsand regulatory events. Moreover, the reaction categories can bearbitrary, or based on, for example, functional criteria, statisticalcriteria, or molecular associations so long as the categories provide anacceptable framework for obtaining a consistency measure between thelegacy-derived network and the empirical data set.

Exemplary reaction categories for the specific embodiment of aregulatory reaction network are described further below in Example IV.Briefly, elements of a regulatory network can be separated into, forexample, three categories based on functional interactions. Thesecategories include, for example, pair-wise regulatory interactions,target-regulator units and regulons. Given the teachings and guidanceprovided herein, categories other than these for regulatory networks aswell as categories for other types of reaction networks can beidentified or generated by those skilled in the art. For example, othertypes of categories can include anabolic or catabolic reactions or cellsignaling functions. The particular type of category will depend on thetype of reaction network to be reconciled and the measure of consistencyselected to be used in the method of the invention.

Consistency of the data sets to be reconciled can be determined by avariety of methods well known to those skilled in the art. Such methodscan be employed to generate a value for each of category or elementwithin a network that can be analyzed for significance. For example, inthe above exemplary reaction categories, consistency measurements forpair-wise interactions can be obtained, for example, by Pearsoncorrelation coefficients whereas consistency measurements fortarget-regulator units can be determined by, for example, multiplecorrelation coefficients. Further, consistency measurements for regulonscan be determined by, for example, the average within reguloncorrelation. Other methods well known in the art also can be employedand include, for example, mutual information-based measures (Cover T M &Thomas J A. Elements of Information Theory, Wiley (1991)), or nonlinearregression methods (Hastie T, Thibshirani R & Friedman J. The Elementsof Statistical Learning, Springer (2001)). The mutual informationmeasures require discretization of the original data, but allowincorporating nonlinear dependencies that are not accounted for byPearson or multiple correlation coefficients. Similarly non-linearcorrelation measures can be used as consistency metrics, but their addedflexibility compared to linear correlation may result in overestimatingthe consistency between empirical data and a proposed network structure.The statistical significance of particular values of a consistencymeasure can be determined to assess whether the legacy data andempirical data constitute a good fit. A high degree of consistencymeasure, such as those that are statistically significant, indicate thatthe two networks, subnetworks or subcomonents reconcile. Further, thosedata sets that reconcile either as to the whole network or a subnetworkthereof indicate a validation of the legacy model whereas those that areinconsistent indicate a divergence between the legacy-derived model andthe empirical data.

The invention further provides a method of refining a biosystem reactionnetwork. The method consists of: (a) providing a mathematicalrepresentation of a biosystem; (b) determining differences betweenobserved behavior of a biosystem and in silico behavior of themathematical representation of the biosystem under similar conditions;(c) modifying a structure of the mathematical representation of thebiosystem; (d) determining differences between the observed behavior ofthe biosystem and in silico behavior of the modified mathematicalrepresentation of the biosystem under similar conditions, and (e)repeating steps (d) and (e) until behavioral differences are minimized,wherein satisfaction of a predetermined accuracy criteria indicates animprovement in the biosystem reaction network.

The method can further include the steps of: (f) determining a behaviorof the biosystem under different conditions, and (g) repeating steps (b)through (e) of the method for refining a biosystem reaction networkunder the different conditions. The method for refining a biosystemreaction network can additionally include repeating steps (f) and (g)until the minimized behavioral differences are exhausted, wherein theimproved biosystem reaction network representing an optimal biosystemreaction network.

The methods of the invention can also be applied in a general process bywhich mathematical representations of biosystems can be improved in aniterative fashion using algorithmic approaches and targetedexperimentation. Many biological systems are incompletely characterizedand additional experimentation can be required to reconstruct a reactionnetwork of these systems. For such a process to converge quickly on anoptimal model, an iterative experimentation can be systematized. FIG. 2b exemplifies such a procedure, which is further described in Example V.

The model building process can begin with a statement of model scope andaccuracy. Alternatively, the model building process can proceed in theabsence of such a predetermined assessment of scope or accuracy butterminated once a desired scope or accuracy is ultimately obtained.

The purpose for building the model leads to specification of expectedaccuracy and the scope of capabilities that the model is to have. Thescope of a model can range from, for example, describing a singlepathway to a genome-scale description of a wild type strain of anorganism. An even broader scope would be to include sequence variationsand thus insist that a model describes all the variants of the wild typestrain.

The accuracy can be based on, for example, qualitative or quantitativecriteria. A useful model can be qualitative and be able to makestatements that predict, for example, that the growth rate of anorganism is reduced when a particular gene product is inhibited under aparticular growth condition. A quantitative model can insist, withinmeasurement error, on predicting the percent reduction in growth rate ofinhibition of all the gene products under one or more growth conditions.The extent of the iterative model-building process is therefore dictatedand predetermined by the user who can specify a required scope andaccuracy of the model to be generated.

A reconstructed biochemical reaction network can be envisioned as amodel of an experimental system. In this regard, it is a duplicate of anactual organism that is capable of flexible manipulation and study underany conditions that is desirable to subject the actual organism to. Oneadvantage of a reconstructed biosystem reaction network, or an in silicoversion thereof, is that it is capable of generating an immense amountof information that characterizes the function and phenotype of theorganism. The accuracy of the in silico model can also be determined by,for example, using the methods described above for reconciliation anddetermining the consistency of the reconstructed network with that ofempirical data obtained from the actual organism. The availability ofboth an actual organism and a reconstructed model of the organism thatis readily manipulable can be used synergistically to harness the powerof in silico models for reliable and accurate predictions of organismbehavior and function.

An approach to reconstructing an in silico model of a biosystem isthrough iterative refinement of a biochemical reaction network. Therefinement of a model can be accomplished by assessing a particularfunction of the actual organism and incorporating into the model newinformation gained from that particular study. Because the model is anduplicate of the organism, deviations in performance from the modelcompared to the actual organism when performed under similar conditionswill yield data indicating that additions, omissions or revisions to thein silico that can account for the deviations. By successive iterationsof studies duplicating conditions that the actual and in silicoorganisms are subjected to, altering the model structure to correct andbe consistent with the empirical data obtained from the actual organismand repeating the condition or subjecting the pair to differentconditions, the accuracy of the model to predict function and phenotypeof the actual organism will successively increase.

Briefly, studies can be performed with the actual organism under definedconditions prescribed by an experiment design algorithm. Similarly, thein silico model that describes the actual organism can be used tosimulate the behavior of the actual organism under the same conditions.Based on the available data at any given time, if the model fails tomeet the desired scope or accuracy requirements, further studies can beperformed to improve the model. These studies can be designed using, forexample, a systematic procedure to step-wise or incrementally probenetwork function. One approach to probe network function can be, forexample, to incrementally move from a robust or validated subsystem ofthe network to less validated parts. Another approach can be, forexample, to target different types functions or different types ofmethods for probing function. Particular examples of such targetedmethods of study include, for example, genomic knock-outs, expressionprofiling, protein-protein interactions, and the like. Therefore, thecontent and capabilities of the in silico model are subject to iterativeupdates.

The decision on what experiments to perform can be determined, forexample, based on the nature of the deviation and the requirements in anaccuracy specification. Deviations can include a gene expression arraythat is not predicted correctly by the model, a set of calculated fluxvalues which does not match the experimentally-determined fluxome undergiven conditions, or a set of phenotypes, for example, growth, secretionand/or uptake rates, which shows discrepancy from model predictions.Experiments which could be performed to resolve such discrepanciesinclude perturbation analysis wherein one or more genes thought to beresponsible for the discrepancy are knocked out, upon which theresulting organism is characterized using transcriptomics, fluxornicsand the like, or environmental analysis wherein one or more component ofthe extracellular environment thought to contribute to model deviationsis removed and the system is re-characterized.

Algorithms can be devised that design such experiments automatically. Analgorithm which can be used in the case of gene expression can be, forexample (1) determine the gene(s) which exhibit a discrepancy from thepredictions of the model, (2) use the regulatory network model toidentify the regulatory protein(s) which control the gene(s) in step(1), (3) knockout one or more genes in the organism which encode one ormore regulatory proteins (4) perform the same transcriptome experimentunder the same environmental conditions but with the new knockoutstrain. A second such algorithm which could be used in the case of ahigh-throughput phenotype study with a reconstructed metabolic networkcould be (1) determine the phenotype(s) which exhibit discrepancy (e.g.,growth rates do not correlate), (2) systematically add all biochemicalreactions, one or more at a time, until the model prediction matches theobserved phenotype(s), (3) identify gene locus/loci with significantsequence similarity to identified enzymes which catalyze the reaction(s)in step (2), (4) clone and characterize the gene in step (3) to verifywhether it can catalyze the predicted reaction(s). The inputs into analgorithm are several, including the present model, the data that it hasbeen tested against, the magnitude and nature of deviations, and soforth. The output from the algorithm can be component experiments ofwhole organism experiments.

An algorithm can identify, for example, missing components in the modeland request that specific biochemical, protein-DNA binding,protein-protein interaction, or enzyme kinetic activity experiments beperformed. As described above, the missing components in the two aboveexamples would be regulatory interactions and identified enzymes. Ifthese studies reveal missing components of the model appropriate modelupdates are performed.

An algorithm can be facilitated by, for example, the inclusion ofadditional data from whole cell behavior. It may request that growth,transcription profiling, metabolic profiling, DNA-transcription factorbinding state, or proteomic experiments be performed under one or moreenvironmental conditions in order to obtain sufficient information toallow model updating.

Given a set of inputs such as gene deletions or environmental inputs,the response of the biochemical reaction network can be examined bothactually and computationally. The actual system will yield an observedresponse characterized through phenomenological pathways of the system,while the model of the actual system will predict a responsecharacterized by the systemic pathways of the system. The observed andcomputed responses can be compared to identify operational pathways asdescribed previously. The difference in the measured and computedcellular functions under the defined conditions where the experiment isperformed can be characterized, for example, as an “error”. Thisdifference corresponds to those systemic pathways that are notoperational. The error can then be used to update the model.

Model update also can be accomplished by, for example, using analgorithm for updating parameters in the model so that the model erroris minimized. As identified in Example VI, an algorithm forcharacterization of a regulatory network can be, for example, (1) obtainthe activity of each protein as predicted by the model, (2) for eachprotein, generate a rule based on the activity of the given proteinwhich results in the correct expression value for T5a, (3) recalculatethe overall expression array for the regulated genes, (4) evaluate thedifference between the criterion for model accuracy by determining thenew model error, and (5) choose the model(s) with the lowest error asthe new model for future iterations. Following optimal model updates areimplemented, the remaining “error” between corrected model predictionsand actual responses can be used to design new studies to further probethe system. The process can be repeated, for example, one or more timesto further update the model based on these new studies and until adesired scope or accuracy is obtained.

Model updates that can minimize error on a round of the iterativereconstruction process can be non-unique or very similar to each otherin generating optimal model updates. To preserve the availability ofsuch data and increase the efficiency of subsequent rounds, alternativemodel updates can be stored, for example, so that they capable of beingretrieved and available for subsequent use on further rounds ofiterative model building. Additionally, a collection of experimentaloutcomes can be stored as a historic record of the behavioral data orphenotypic data that has been obtained on a particular organism. Modelupdates and design algorithms can be optionally capable of querying thisdatabase during execution. Various other records and system data can bealternatively stored for later efficient utilization in one or moresteps of the iterative process. Such computational approaches are wellknown in the art and can be routinely implemented given the teachingsand guidance provided herein.

Further, combinations and permutations of the various methods of theinvention can be combined in any desired fashion to facilitate the modelbuilding process or to augment a purpose or implementation of themethod. Additionally, single or other “off-line” studies can beperformed and the information generated used in any of the methods ofthe invention to facilitate, augment or optimize results orimplementation. For example, in addition to studies designed for theiterative process, in some cases specific pair-wise interactions amongmolecules can be probed in separate off-line studies to furthercharacterize individual molecular components.

Advantageous properties of the iterative model-building procedureinclude convergence of system components into an operative and optimalrepresentation of the actual organism and efficiency of constructingsuch a model. Efficiency in convergence is important since it willminimize the number of studies that need to be performed.

The following examples are intended to illustrate but not limit thepresent invention.

Example I Decomposing a Set of Phenomenological Flux Distributions forthe E. coli Core Metabolic Network in Order to Identify OperationalExtreme Pathways

This example shows how a set of phenomenological pathways (fluxdistributions) can be decomposed into dominant modes these modes can becompared with a set of systemic pathways (extreme pathways) to identifyoperational reaction pathways of a metabolic reaction network (E. colicore metabolism).

An in silico-generated metabolic flux profile of core metabolism in E.coli was prepared. The reactions were taken from table 6.3 of Schilling,“On Systems Biology and the Pathway Analysis of Metabolic Networks,”Department of Bioengineering, University of California, San Diego: LaJolla. p. 198-241 (2000), with the exception that reaction pntAB was notincluded, and instead of T3P2 in reaction tktA2, T3P1 was used. Thereaction list is tabulated in Table 1.

The flux profile, which is the input matrix for Singular ValueDecomposition (SVD) analysis, consists of 57 fluxes (rows) and 7conditions in each phase (columns). The phase plane for succinate forthis system is presented in FIG. 3; generation of Phase Planes isdescribed in (Edwards J S, Ramakrishna R, Palsson B O. Characterizingthe metabolic phenotype: a phenotype phase plane analysis. BiotechnolBioeng. 2002 Jan. 5;77(1):27-36). The points on FIG. 3 were chosen todefine the upper limit of oxygen and succinate available to the system.Each point, therefore, represents a different condition (or column ofthe flux matrix) in constructing the flux profile.

SVD analysis was performed on each phase (each of the 7 conditions)separately. The decomposition of the flux matrix, A, results in threedistinct matrices U (the left singular matrix), E (singular valuematrix), and V (right singular matrix):

A=U·∈·ENT

For phase I of the phase plane, the flux distribution matrix wasgenerated with the E. coli core metabolism using the oxygen andsuccinate input values that are tabulated next to FIG. 4. The points lieon phase I as shown.

SVD analysis on the flux matrix revealed that there is only one dominantmode in phase I as demonstrated by the singular value fractions shown inFIG. 5. Therefore, there is a common expression that dominates nearlyall of the system's behavior in this phenotypic phase, which can becalled a phase invariant singular value.

The contribution level of each condition (i.e., each point shown inPhase I of the phase plane) is shown in FIGS. 6 and 7 for various modesobtained from SVD. The weight that each mode has on the overallcontribution of a pathway is seen by how far the curve of that mode isfrom the zero contribution level (horizontal zero level). Also, for eachmode, the expression level increases with the condition number whichshows how fluxes increase in the pathway represented by that mode. Theserepresentations provide information regarding where on the phase planethe point lies relative to other points (i.e., at a higher or lowergrowth rate). Thus, not only is information provided about the dominantmodes, but also additional information is provided on biomass productionrate. The slope of the first dominant mode (“first mode”) shouldcorrespond to the slope of growth rate. The first mode captures nearly100% of the overall contribution.

To compare the results from SVD and with the results from pathwayanalysis, extreme pathways of the core E. coli system were calculated,using succinate as the sole carbon source. The reduced set of extremepathways for succinate is presented in Table 2 (adopted from Schilling,supra (2000), Table 6.6) and shown in FIG. 8.

For the Phase I analysis described above, to compare the extremepathways with the 1st mode, the genes were arranged in the same orderand fluxes were normalized by succinate uptake rate. The angles betweenthe 1st mode and each of the 12 extreme pathways were calculated andsorted in descending order. Also, the number of different fluxes (i.e.,fluxes that are zero in one case and non-zero in the other case or haveopposite signs) and the net flux difference between the first mode andeach pathway were calculated and sorted in the same fashion. Table 3provides the results of this analysis.

This analysis shows that the first mode in phase I is exactly equivalentto the line of optimality (i.e., P_(—)33). It also shows that followingthis pathway, the first mode is the closest to pathways 32, 30, and soon. Therefore, column angle not only shows what pathways best describeflux distribution in phase I in the order of similarity, but it alsoshows how similar they are amongst themselves.

The analysis was repeated for Phases II and III, and for all phasestogether. When all phases were analyzed by SVD together, again a singledominant mode was identified (FIG. 14), with relatively low entropy(4.80E-3). The angle between this mode and each of the 12 extremepathways was calculated. Table 4 provides the results of this analysis.By this analysis, the dominant mode was closest to extreme pathways 33and 32 shown in Table 2.

Example II Identifying Human Red Blood Cell Extreme PathwaysCorresponding to Physiologically Relevant Flux Distributions

This example shows how a set of phenomenological pathways (fluxdistributions) generated by a kinetic model can be compared with themodal decomposition of a set of systemic pathways (extreme pathways) toidentify dominant regulatory modes of a metabolic reaction network(human red blood cell metabolism).

The extreme pathways of the red blood cell (RBC) metabolic network havebeen computed (Wiback, S. J. & Palsson, B. O. Biophysical Journal 83,808-818 (2002)). Here, SVD analysis was applied to the extreme pathwaymatrix, P, formed by these pathways. A full kinetic model of the entiremetabolic network of the RBC has been developed (Jamshidi, N., Edwards,J. S., Fahland, T., Church, G. M., Palsson, B. O. Bioinformatics 17,286-7 (2001); Joshi, A. & Palsson, B. O. Journal of Theoretical Biology141, 515-28 (1991)), and was used to generate flux vectors (v) forphysiologically relevant states. These flux vectors were decomposedusing the modes obtained from SVD of P.

The rank of the V_(max)-scaled RBC extreme pathway matrix, P, was 23.The first mode represents 47% of the variance (FIG. 10F). Combined, thefirst five modes capture 86% of the variance of the solution space,while the first nine modes capture 95% of its variance.

The first five modes of P are shown on the metabolic maps in FIG.10(A-E). The first mode shows low flux values though the adenosinereactions, higher fluxes through the glycolytic reactions, with an exitthrough the R/L shunt, and the highest flux levels through the pentosephosphate pathway. This map describes the principal variance of thesteady-state solution space. The subsequent modes describe the nextdirections of greatest variance in the steady-state solution space (FIG.10). Movement along a mode in the positive direction corresponds toincreasing the fluxes shown in red and decreasing those shown in green.Since the modes are required to be orthogonal, they specificallydescribe the directions of variance in the cone that are independentfrom each other. The subsequent modes can be interpreted biochemicallyas follows:

The second mode describes the flux split between glycolysis and thepentose phosphate pathway. If the contribution of this mode is added tothe first mode it would lead to decreased flux through the pentosephosphate pathway and reduced production of NADPH. The increasedglycolytic flux exits through the Rapoport-Leubering (R/L) shunt leadingto decreased ATP production since ATP is used in upper glycolysis andnot recovered in lower glycolysis. The production of NADH increases.

The third mode describes the glycolytic pathway down to pyruvate withproduction of ATP and NADH. It also describes lowered dissipation of ATPas a consequence of AMP dissipation by AMPase. This mode has asignificant ATP production.

The fourth mode describes the flux split between lower glycolysis andthe R/L shunt. It thus naturally interacts biochemically with the secondmode. The fourth mode further describes an increase in ATP dissipationvia the AMPase-AK cycle leading to little net production of ATP, andinteracts with mode three.

The fifth mode is actually one of the extreme pathways. It describesimporting pyruvate and converting it to lactate, thus dissipating oneNADH. It thus will be important in balancing NADH redox metabolism.

As shown below the first five modes account for most of the RBC'sphysiological states.

The nominal state (no additional metabolic load) of the red blood cellmetabolic network was calculated using a full kinetic model and is shownon the RBC metabolic map (FIG. 10G). This nominal physiologic steadystate of the RBC was decomposed into 23 modes (FIG. 10H). The relativeerror remaining in the reconstructed solution after the addition of eachmode to the reconstruction of the nominal steady state fell sharply(FIG. 10H). After the contribution of the first five modes, thereconstructed nominal state had a relative error of 0.013 (RE(5)=0.013).

An inspection of the first five modes (FIG. 10A-E) demonstrates how theyreconstruct the physiologic steady state solution. Relative to the firstmode (FIG. 10A), adding the second mode (FIG. 10B) increases the fluxthrough the first half of glycolysis, decreases the flux through thepentose phosphate reaction, and decreases NADPH production, all of whichmoves the reconstructed solution significantly towards the physiologicsteady state (FIG. 10G). Adding the third mode (FIG. 10C) increases theflux through all of glycolysis, particularly through lower glycolysis.The addition of the fourth mode (FIG. 10D) appropriately decreases theamount of 23DPG that is produced and instead sends that flux throughlower glycolysis. Finally, the addition of the fifth mode increases theflux from pyruvate to lactate, which leads essentially to the steadystate solution where lactate is the primary output of glycolysis. Thus,the significant features of the physiologic steady state are capturedwithin the first five modes. A regulatory structure that can move thesolution along these five independent directions in the solution spacewill be able to generate the desired physiological state.

Steady-state flux distributions for two load levels of NADPH, ATP, andNADH were calculated using the RBC kinetic model. These pairs of loadlevels each represented the maximum load the in silico RBC couldwithstand, as well as one value chosen within the tolerated load range.NADPH loads simulate physiologic states corresponding to the red bloodcell's response to oxidative free radicals. The maximum NADPH load is2.5 mM/hr. The ATP loads simulate conditions of increased energy loads,such as in hyperosmotic media. The maximum ATP load is 0.37 mM/hr. TwoNADH loads, important for methemoglobin reduction in the RBC, were alsoapplied. These six computed flux vectors thus represent extremephysiological states of the RBC, and help designate the region ofphysiologically meaningful states within the steady-state solutionspace.

The modal composition of each of the six “stressed” steady state fluxsolutions gives significant weighting to the first five modes (FIG.10H). In addition, some “fine tuning” appears in modes 7 to 11. All ofthe other modes are essentially insignificant in reconstructing thesesolutions to the RBC kinetic model.

The application of metabolic loads changed the weighting of the firstfive modes to reconstruct the appropriate metabolic flux distribution(FIGS. 10H,I). Increases in the NADPH load resulted in a substantialincrease of the weighting on the first mode, increasing the flux throughthe pentose phosphate reactions and thus elevating the production ofNADPH. The weightings on the second, third, fourth, and fifth modesdecrease with the application of higher NADPH loads largely because asNADPH production is maximized the flux distribution approaches that ofthe first mode. The reduction in the weighting of the second mode,however, is the most dramatic. The application of increasing ATP loadsresulted in little change in the values of the weightings on all of thefirst five modes. The application of ATP load is handled in the RBC by adecrease in an ATP-consuming futile cycle, with the ATP generatedinstead being used instead to satisfy the load imposed upon the cell.Thus, the usage of an ATP-dissipating futile cycle in the unstressedstate of the RBC acts to dampen the effects of changing ATP loads,allowing the RBC to respond to changing ATP loads with little change inthe overall flux distribution in the cell. Related experimental findingshave demonstrated that the concentration of ATP in the RBC does notchange much as environmental conditions change within specified limits,as a result of this buffer, but then changes dramatically when the ATPload is pushed beyond those limits. The application of the NADH loadsresulted in a significant decrease of all the mode weightings becausethe length of the flux vector decreases. The weighting on the fifth modedecreased most dramatically since it consumes NADH when utilized in thepositive direction and thus had needed to be scaled down.

After the inclusion of the first five modes, the relative error (RE(5))of all the reconstructed solutions ranged from 0.005 to 0.018. In allsix cases, the first five modes reconstructed at least 98% of the steadystate solutions. Thus, the physiologically relevant portion of thesteady-state solution space appears to be only 5 dimensional, andtherefore there are effectively only five degrees of freedom to theproblem of regulating red cell metabolism.

Decomposition of the extreme pathway vectors into the modes shows thatthe most important mode, in the reconstruction, is often not one of thefirst five modes (FIG. 10J). Thus, many portions of the allowablesolution space, as defined by the extreme pathways, are poorlycharacterized by the first five modes, which effectively reconstructeach solution to the full RBC kinetic model. Thus, many of the extremepathways are physiologically irrelevant and they can be identified usingSVD of P, if the approximate location of physiologically meaningfulsolutions is known.

Study of regulation of metabolism has historically focused on theidentification and characterization of individual regulatory events. Nowthat we can reconstruct full metabolic reaction networks we can addressthe need for regulation from a network-based perspective. This study hasfocused on interpreting regulation from a network-based perspectiveusing singular value decomposition of the extreme pathway matrix forhuman red blood cell metabolism. Two main results were obtained. First,the dominant modes obtained by SVD interpret RBC metabolic physiologywell. Second, the first five modes effectively characterize all therelevant physiological states of the red cell.

RBC metabolic physiology is well interpreted by the dominant modesobtained from SVD. Using the calculated modes, seven physiologicallyrelevant solutions to the full RBC kinetic model were reconstructed. TheRE(5) for these solutions was within 0.017. Thus, the first five modescan be used to essentially completely recapture each of thephysiologically relevant kinetic solutions. However, most of the extremepathways could not be reconstructed to such a high degree by the firstfive modes. Thus, the first five modes represented the space relevant tosolutions to the full kinetic model better than they did to the space asa whole, even though they were calculated to optimize their descriptionof the entire space. This fact suggests that developingconstraints-based methods that take into account kinetics andmetabolomics will result in defining a solution space that is muchsmaller than the space circumscribed by the extreme pathways.

The results obtained herein were based on the topology of the metabolicnetwork and knowledge of some V_(max) values. The next step to bridgethe gap between the network-based results and the study of individualregulatory events is to find the best ways to pair candidate regulatorymolecules and the systemic regulatory needs. In control theory this isknown as the ‘loop-pairing’ problem (Seborg, D. E., Edgar, T. F. andMellichamp, D. A. Process Dynamics and Control (Wiley, N.Y., 1989)). Asa part of its solution we may have to relax the need for strictorthonormality of the modes and look for oblique modal bases that aremore in line with the underlying biochemistry of the network.

Taken together, this study presents a network-based approach to studyingregulatory networks and defines the degrees of freedom of the regulatoryproblem. This method calculates the modalities needed to enable themetabolic network to navigate its solution space and thus could be usedto infer candidate regulatory loops of metabolic systems for which theregulation is largely unknown. Further, based upon their contribution tothe steady-state solution space, these regulatory loops can potentiallybe ordered in terms of their importance to the reconstruction of thespace. Network-based approaches to studying regulation, such as the oneoffered herein, complement component-based studies and provide apotential framework to better understand the interaction of regulatorycomponents needed to achieve the regulatory demands of the cell.

Example III In Silico Assessment of the Phenotypic Consequences of RedBlood Cell Single Nucleotide Polymorphisms

The following example illustrates the application of the describedmethods to analysis of phenomenological pathways defined throughpathological data.

The Human Genome Project (HGP) is now essentially complete. One resultof the HGP is the definition of single nucleotide polymorphisms (SNPs)and their effects on the development of human disease. Although thenumber of SNPs in the human genome is expected to be a few million, itis estimated that only 100,000 to 200,000 will effectively define aunique human genotype. A subset of these SNPs are believed to be“informative” with respect to human disease (Syvanen, A., 2001.Accessing genetic variation: Genotyping single nucleotide polymorphisms.Nat Rev Genet 2: 930-942). Many of these SNPs will fall into codingregions while others will be found in regulatory regions. The humangenotype-phenotype relationship is very complex and it will be hard todetermine the causal relationship between sequence variation andphysiological function. One way to deal with this intricate relationshipis to build large-scale in silico models of complex biological processes(FIG. 12). Defects or alterations in the properties of a singlecomponent in complex biological processes can be put into context of therest by using an in silico model. In this work, recent data on SNPs inkey red blood cell enzymes (FIG. 12 a) and corresponding alterations intheir kinetic properties (FIG. 12 b) were used in an in silico red bloodcell model (FIG. 12 c) to calculate the overall effect of SNPs on wholecell function (FIG. 12 d).

The study of variations in the kinetic properties of red blood cellenzymes is not merely an academic study of the quality of a mathematicalmodel, but has real utility in the clinical diagnosis and treatment ofenzymopathies and can provide a link to the underlying sequencevariation (FIG. 12). Here, an in silico model is used to study SNPs intwo of the most frequent red blood cell enzymopathies:glucose-6-phosphate dehydrogenase (G6PD) and pyruvate kinase (PK).

For both enzyme deficiencies, clinical data was obtained from thepublished literature to determine measured values for the variouskinetic parameters (V_(max)'s, Km's, Ki's) associated with eachclinically diagnosed variant. These numerical values were then used inthe in silico model (Jamshidi, N., Edwards, J. S., Fahland, T., Church,G. M., Palsson, B. O. Bioinformatics 17, 286-7 (2001)) and sensitivitiesto various oxidative and energy loads (above normal, baseline values)were simulated. The results are interpreted with respect to the geneticbasis of the enzymopathy in an attempt to establish a direct linkbetween the genotype and phenotype (FIG. 12).

Glucose-6-phosphate dehydrogenase (G6PD) catalyzes the first step in theoxidative branch of the pentose pathway (FIG. 12 c) and is thus ofcritical importance in maintaining the red blood cell's resistance tooxidative stresses. G6PD is the most common erythrocyte enzymopathy,affecting approximately 400 million people worldwide.

G6PD from normal patients and patients with hemolytic anemia have beencharacterized on the molecular level. A total of 61 G6PD class Ivariants have been described at the molecular level. Of the 61 class Ichronic variants, 55 are the result of SNPs involving amino acidchanges, 5 result from frame deletions and one results from a splicingdefect (Fiorelli, G., F. M. d. Montemuros and M. D. Cappellini,Bailliere's Clinical Haematology 13: 35-55 (2000)).

Clinically diagnosed SNPs cluster around important, active regions ofG6PD enzyme including the dimer interface and substrate binding sites(FIG. 13 a). Numerical values of G6PD kinetic parameters were varied insilico to determine the sensitivity of red blood cell metabolicfunctions to these changes in enzyme function. The most sensitiveparameters were found to be V_(max) and Ki-NADPH. The NADPH/NADP ratioproved to be the most informative indicator of metabolic status as itwas the most sensitive to changes in these two parameters and it givesan indication as to the oxidative state of the cell (Kirkman, H. N., G.D. Gaetani, E. H. Clemons and C. Mareni, Journal of ClinicalInvestigation 55: 875-8 (1975)). For each documented variant thereappears to be no direct correlation between V_(max) and Ki-NADPH (FIG.13 b). Clinically, G6PD deficiencies are broken down into two maincategories: chronic and non-chronic hemolytic anemia. Chronic cases showclinical symptoms and are very sensitive to the environment. Non-chroniccases appear normal under homeostatic conditions but can experienceproblems when subjected to large oxidative stresses (Jacobasch, G., andS. M. Rapoport, in Molecular Aspects of Medicine (1995)). For thisstudy, kinetic data for 12 chronic and 8 non-chronic cases from Yoshidaand 19 chronic cases from Fiorelli were used (Fiorelli, G., F. M. d.Montemuros and M. D. Cappellini, Bailliere's Clinical Haematology 13:35-55 (2000); Yoshida, A., pp. 493-502 in Glucose-6-PhosphateDehydrogenase, Academic Press 1995).

Under normal conditions (i.e., oxidative load, V_(ox)=0) there aredifferences between the chronic and non-chronic groups with the chronicgroup having a somewhat lower homeostatic steady state NADPH/NADP ratiothan the non-chronic group. When subjected to an oxidative load(V_(ox)>0), noticeable differences between the two groups (chronic andnon-chronic) appear (FIG. 14). The NADPH/NADP ratio at the maximumtolerated oxidative load (V_(ox)=max value) correlates with this ratioin the un-stressed situation (V_(ox)=0). The group of chronic hemolyticanemia patients are clearly separated from the normal and non-chronicgroup. A number of the chronic cases can only withstand a very modestoxidative load. Of the variant cases studied, a handful have beencharacterized at the molecular (amino acid) level (Table 5). Of thecases considered, most of the single base changes in the chronic (classI) variants occur at or near the dimer interface (exons 10,11 and 6,7)or near the NADP binding site, leading to an impaired ability to respondto systemic oxidative challenges.

Pyruvate kinase (PK) is a key glycolytic regulatory enzyme. There haveonly been about 400 documented variants since PK's first description in1961 (Jacobasch, G., and S. M. Rapoport, in Molecular Aspects ofMedicine (1996); Tanaka, K. R., and C. R. Zerez, Seminars in Hematology27: 165-185 (1990); Zanella, A., and P. Bianchi, Balliere's ClinicalHematology 13: 57-81 (2000)). PK accounts for 90% of the enzymedeficiencies found in red blood cell glycolysis. It is autosomalrecessive where clinical manifestations appear only in compoundheterozygotes (2 mutant alleles). There are four isozymes: L, R, M1, andM2, with the R type being exclusive to the red blood cells. PK isencoded by the PK-LR gene on chromosome 1q21. The kinetics of the enzymehave been extensively studied (Otto, M., R. Heinrich, B. Kuhn and G.Jacobasch, European Journal of Biochemistry 49: 169-178 (1974)). PKactivity is regulated by F6P, ATP, Mg, and MgATP. Anemic heterzygoteshave 5-40% of normal PK activity.

A summary of the PK variants is presented in Table 6. The Sassarivariant only has a SNP (cDNA nt 514) transversion of a G to a Cresulting in a change of Glu to Gln at aa 172 which is in between the β1and β2 in the B domain. Here a basic (negatively charged amino acid) isreplaced by a polar uncharge amino acid. Parma has 2 SNPs, one at aa 331or 332 and another at aa 486 or 487, neither of whose amino acid changeshave been elucidated yet. Soresina and Milano share the amino acidchange Arg to Trp at aa 486 (positively charged to non-polar). Bresciahas a deletion of Lys at aa 348 and another change at aa 486 or 487 thathas not been defined yet. Mantova has an exchange at amino acid 390 Aspto Asn (negatively charged to polar uncharged). (Bianchi, P., and A.Zanella, 2000 Hematologically important mutations: red cell pyruvatekinase. Blood Cells, Molecules, and Diseases 15: 47-53; Zanella, A., andP. Bianchi, Balliere's Clinical Hematology 13: 57-81 (2000)).

Unlike for G6PD, the characterized PK SNPs are scattered throughout theprotein coding region and do not appear to cluster near thecorresponding active site of the enzyme. The documented kinetic valuesfor the main kinetic parameters V_(max) and KPEP are shown (FIG. 15 a).Similar to the G6PD variants, there is not a clear correlation betweenchanges in the numerical V_(max) and KPEP amongst the PK variants (FIG.15 b). Although changes in KADP are also documented for each variant andaccounted for in the simulations, increases or decreases in its valuedid not significantly affect the red blood cell's steady statemetabolite concentrations or its ability to withstand energy loads (datanot shown). Changes in KPEP and V_(max) influence the concentration ofATP and 2,3DPG most significantly. When increased energy loads (Y_(e)>0)are applied in silico, differences between the variants are observed.The ratio between the ATP concentration at maximum tolerated load(ve=max value) and the ATP concentration in the unchallenged state(V_(e)=0) varies approximately linearly with the maximum tolerated loadwhen all the variants are evaluated (FIG. 15 c). Thus the variants thattolerated the lowest maximum load have a [ATP]max/[ATP]no load ratioclose to unity indicating their sharply diminished ability to deviatefrom the nominal homeostatic state. Interestingly, the computed energycharge (EC=(ATP+½ADP)/(ATP+ADP+AMP)) (Atkinson, D. E., 1977).

Cellular energy metabolism and its regulation. (Academic Press, NewYork) stays relatively constant (FIG. 15 d). This result indicates thatred blood cell metabolism strives to maintain its EC within thetolerated load range, thus allowing for an energetically consistentmetabolic function.

Sequence variations in coding regions for metabolic enzymes can lead toaltered kinetic properties. The kinetic properties of enzymes aredescribed by many parameters and a single SNP can alter one or many ofthese parameters. For the variants of G6PD and PK considered here, thereappears to be no clear relationship between their kinetic parameters asa function of sequence variation. Thus consequences of sequencevariations on the function of a gene product must be fully evaluated toget a comprehensive assessment of the altered biochemical function.

The consequences of many simultaneously altered enzyme properties mustin turn be evaluated in terms of the function of the enzyme in thecontext of the reaction network in which it participates. The assessmentof sequence variation on biochemical and kinetic properties of enzymesmay seem difficult and this challenge is currently being addressed(Yamada, K., Z. Chen, R. Rozen and R.G. Matthews, Proc Natl Acad Sci USA98: 14853-14858 (2001)), but the assessment of sequence variation onentire network function is even more complicated. This highly complexand intricate relationship between sequence variation and networkfunction can be studied through the use of a computer model. Here wehave shown that a large number of variants in red blood cell G6PD and PKcan be systematically analyzed using an in silico model of the red bloodcell. Correlation between sequence variation and predicted overall cellbehavior is established, and in the case of G6PD, it in turn correlateswith the severity of the clinical conditions.

Example IV Consistency Between Known Regulatory Network Structures andTranscriptomics Data

The following example illustrates the use of the described methods tovalidate and expand known regulatory network structures by reconcilingthese structures with large-scale gene expression data sets.

The availability of large genome-scale expression data sets hasinitiated the development of methods that use these data sets to inferlarge-scale regulatory networks (D'Haeseleer, P., Liang, S. and Somogyi,R Bioinformatics 16:707-26 (2000); de Jong, H. J. Comput. Biol. 9:67-103(2002); Yeung, M. K., Tegner, J. & Collins, J. J. Proc. Natl. Acad. Sci.USA 99:6163-8 (2002)). Alternatively, such regulatory network structurescan be reconstructed based on annotated genome information, well-curateddatabases, and primary research literature (Guelzim, N., Bottani, S.,Bourgine, P. and Kepes, F. Nat. Genet. 31, 60-3. (2002); Shen-Orr, S.S., Milo, R., Mangan, S. & Alon, U. Nat. Genet. 31, 64-8 (2002)). Herewe examine how consistent existing large-scale gene expression data setsare with known genome-wide regulatory network structures in Echerichiacoli and Saccharomyces cerevisiae. We find that approximately 10% of theknown pair-wise regulatory interactions between transcription factorsand their target genes are consistent with gene expression data in bothorganisms. We show that accounting for combinatorial effects due tomultiple transcription factors acting on the same gene can improve theagreement between gene expression data and regulatory networkstructures. We also find that regulatory network elements involvingrepressors are typically less consistent with the data than onesinvolving activators. Taken together these results allow us to defineregulatory network modules with high degree of consistency between thenetwork structure and gene expression data. The results suggest thattargeted gene expression profiling data can be used to refine and expandparticular subcomponents of known regulatory networks that aresufficiently decoupled from the rest of the network.

The known genome-scale transcriptional regulatory network structures foryeast (Guelzim, N., Bottani, S., Bourgine, P. & Kepes, F. Nat. Genet.31, 60-3. (2002)) and E. coli (Shen-Orr, S. S., Milo, R., Mangan, S. andAlon, U. Nat. Genet. 31, 64-8 (2002)) were obtained and pre-processed toremove autoregulation. These structures were represented as graphs withdirected regulatory interaction edges between a regulator node(typically a transcription factor) and a target gene node, with the modeof regulation (activation, repression, or both) indicated for eachinteraction. The yeast network has 108 regulatory genes regulating 414target genes through 931 regulatory interactions, whereas the E. colinetwork has 123 regulatory genes regulating 721 target genes through1367 regulatory interactions. We used data from a total of 641 diversegene expression profiling experiments organized into five separate datasets for yeast and 108 experiments organized into three separate datasets for E. coli.

There were three basic types of regulatory network elements analyzed inthis study: 1) pair-wise regulatory interactions, 2) target-regulatorunits, and 3) regulons. A target-regulator unit (TRU) is defined as asingle target gene together with all of its transcriptional regulators.A regulon is defined as the set of all target genes for a singletranscriptional regulator. For each instance of the individual networkelements present in the network, we computed a consistency measurebetween a particular gene expression data set and the network elementstructure. The particular measures we used were Pearson correlationcoefficients for pairwise interactions, multiple coefficients ofdetermination for TRUs, and average within regulon correlation forregulons. The statistical significance of a particular value of aconsistency measure was determined by a randomization procedure.

The simplest elements in the regulatory network are pair-wiseregulator-target interactions. Overall only a relatively small fraction(less than 10% at P<0.01) of pairwise interactions are in agreement withthe gene expression data given the criteria stated above. In particular,virtually none of the repressor-target interactions are supported by anyof the gene expression data sets examined. Most repressors actually havepositive correlation with the expression of their target genes—notnegative as would be expected for a repressor. These results forrepressing pair-wise interactions highlights the problems associatedwith detecting transcripts expressed at a low level as a result of atranscriptional repressor bound to the promoter of the target gene.

Analysis of pair-wise correlations could overestimate correlationsbetween transcription factor and target gene expression levels in thepresence of transcriptional feed-forward loops. In such cases two ormore transcription factors act on the same gene, but some of them(primary regulators) also regulate another (secondary) regulatordirectly. Feed-forward loops can lead to an indirect effect by which thesecondary regulator-target correlation is solely due the influence ofthe primary regulators. In the framework used here, this effect can beaccounted for by replacing standard correlation coefficients withpartial correlation coefficients for secondary regulator-targetinteractions. Although there is a significant number of feed-forwardloops in both networks (240 in yeast, 206 in E. coli), the overalleffect of accounting for feed-forward loops is small (0-3 percentagepoints).

Target-regulator units represent more complex combinatorial effects thanfeed-forward loops. The percentage of TRUs consistent with geneexpression data is higher than the percentage of consistent pair-wiseinteractions for E. coli at all confidence levels. This result indicatesthat combinatorial effects between transcription factors play asignificant role in many cases. Conversely for TRUs in yeast, we do notobserve a significant change in the percentage of units in agreementwith expression data compared to the calculations that considered onlypairwise interactions.

TRUs can be categorized by the number of regulators that act on thetarget gene. In yeast, the TRUs with four regulators are in general bestsupported by the gene expression data. These four-regulator TRUs includegenes participating in diverse cellular functions including nitrogenutilization, oxygen regulation, and stress response. Hence the highdegree of consistency observed for four-regulator TRUs does not appearto be solely due to a particular subcomponent of the network, but is amore general feature of the network structure. In E. coli, no cleardependence between the number of regulators and the fraction ofconsistent TRUs can be detected.

In order to investigate the agreement between regulatory networkstructures and gene expression data from a different perspective thatdoes not assume correlation between the expression levels oftranscription factors and their target genes, we studied the coherenceof gene expression within known regulons. A large fraction of regulons(over 40%) have coherent gene expression in both yeast and E. coli evenfor the most stringent confidence level (P<0.001) in at least one dataset. This result indicates that a clustering-like approach to analyzinggene expression data can indeed be expected to be successful indetecting truly co-regulated genes. The most interesting feature of thiscalculation is the relatively low level of regulon coherence forregulons regulated by transcriptional repressors in yeast. In contrast,E. coli regulons controlled by repressors tend to be more coherent thanthose controlled by activators.

All the results described above for both yeast and E. coli can bedisplayed on a map of the regulatory network (FIG. 16). This datadisplay allows identifying subcomponents of the networks that have highdegree of agreement with the gene expression data sets analyzed. Forexample in yeast the nitrogen utilization (I in FIG. 16 a) and oxygenresponse (O) systems have many highly consistent elements, but theelements in the carbon utilization (C) network are generally notconsistent with the gene expression data. Similarly in E. colicomponents such as the flagellar biosynthesis network (F in FIG. 16 b)are highly consistent, but the carbon utilization (C) network again doesnot have many consistent network elements.

Some of the variability in consistency between regulatory networkstructures and gene expression data appears to be due to the types ofdata sets utilized in this work. For example, the DNA repair system inE. coli was specifically activated in one of the gene expression datasets and the response to nitrogen depletion was studied in one of theyeast data set. However, there are also general network structuralfeatures that appear to influence consistency. The most prominentfeature is the tendency of relatively isolated subcomponents of thenetwork such as flagellar biosynthesis in E. coli or nitrogenutilization in yeast to be consistent with gene expression data whereashighly interconnected components such as carbon utilization regulationare typically inconsistent. However, not every isolated sub-network isconsistent indicating that the network reconstruction may be incompleteand these subnetworks may in fact be more strongly connected to otherparts of the network than is currently known.

Taken together, the results shown here indicate that combininginformation on known regulatory network structures with gene expressiondata is a productive way to validate and expand regulatory networksstructures. It is important to note that, because the overall level ofconsistency was generally found to be low, genome-scale reconstructionof regulatory networks based on gene expression data alone does notappear to be feasible, even if large quantities of data is available asis the case for yeast. The results show that different features of thenetwork structure influence consistency. In particular, we observe thatnetwork elements involving repressors (pair-wise interactions, regulons)are typically less consistent than those involving activators indicatingthat reconstruction of these types of network components would pose achallenge. Further, in yeast TRUs with four regulators are generallymore consistent than other types of TRUs indicating that in such casesthe known network structure appears to be sufficiently complete whereasfor the TRUs with fewer regulators there may be regulators missing. Thediscovery of highly consistent network subcomponents indicates that agene expression data based reconstruction of regulatory networks can bea powerful strategy for particular subcomponents that are sufficientlyisolated and for which sufficient quantities of relevant data isavailable. Future availability of other high-throughput data types suchas genome-wide DNA-binding site occupancy data (Ren, B. et al. Science290:2306-9. (2000)) will further improve the prospects of suchreconstruction as additional data types can be used to resolveinconsistencies. The full utilization of all high-throughput data types,however, will require the combination prior biological knowledgeextracted from databases and literature with the statistical analysis ofthe large-scale data sets. Thus, full reconstruction of regulatorynetworks will rely on a combination of ‘bottom-up’ and ‘top-down’approaches with targeted prospective experimentation to successivelyresolve inconsistencies between the two. Ultimately, all such data typesare expected to be reconciled in the context of genome-scale in silicomodels of regulatory networks that can be used to analyze, interpretedand ultimately predict their function.

Example V Iterative Refinement of a Regulatory Network Model

The purpose of this example is to illustrate how the methods describedcan be used for regulatory network identification, improvement and theidentification of regulatory states in regulatory or combinedregulatory/metabolic models.

The “bottom-up” approach to genome-scale transcriptional regulatorynetwork model reconstruction is initiated by incorporation of knowledgeinto a computational model to analyze, interpret and predict phenotype.The process begins with first pass reconstruction of metabolic andtranscriptional regulatory networks for the organism of interest.Reconstruction of such genome-scale models has been described elsewherein detail (Covert M. W., Schilling C. H., Famili I., Edwards J. S.,Goryanin II, Selkov E., Palsson B. O. Trends Biochem Sci 26:179-86(2001); Covert M. W., Schilling C. H., Palsson B., J Theor Biol213:73-88 (2001)) and leads to the representation of metabolic behavioras a linear programming problem, with a matrix describing all knownmetabolic reactions, and certain measured parameters (e.g., maximumuptake rates, biomass composition) defined as constraints on themetabolic system. Transcriptional regulatory behavior is represented asa set of regulatory rules written as Boolean logic statements. Theserules are dependent on environmental and internal conditions anddetermine the expression and/or repression of various metabolic genes inthe metabolic network.

The regulatory and metabolic models are integrated as the outcomes ofthe logic statements impose time-dependent constraints on the metaboliclinear programming problem. The outcome of the linear programmingproblem is then used to recalculate environmental conditions (Varma A.,Palsson B. O., Appl Environ Microbiol. 60:3724-31 (1995); Covert M. W.,Schilling C. H., Palsson B. J Theor Biol. 213:73-88 (2001)), and theBoolean logic equations are reevaluated.

The Boolean logic rules are derived from the primary literature torepresent the conditions required for expression of a particular gene orset of genes. Experimental studies are examined to obtain a set ofpotential transcription factors for all known promoters of expression ofa particular target gene. The presence of multiple promoters from whichtranscription may occur indicates an OR relationship, and the presenceof two interacting transcription factors which effect one promoterindicates an AND relationship. For example, if gene A has two promoters,one of which is activated by transcription factor X and the other whichis repressed by the integrated product of transcription factors Y and Z,then a rule may be derived which states that A is transcribed IF (X) ORNOT (Y AND Z).

Such a model is in process of being built for E. coli. For thisorganism, a genome-scale metabolic network model had already beenreconstructed (Edwards J. S., Palsson B. O., Proc Natl Acad Sci USA.97:5528-33 (2000)). The regulatory network model was first implementedfor core metabolic processes. The first combined metabolic/regulatorymodel accounts for 149 genes, the products of which include 16regulatory proteins and 73 enzymes. These enzymes catalyze 113reactions, 45 of which are controlled by transcriptional regulation. Thecombined metabolic/regulatory model can predict the ability of mutant E.coli strains to grow on defined media, as well as time courses of cellgrowth, substrate uptake, metabolic by-product secretion and qualitativegene expression under various conditions, as indicated by comparison toexperimental data under a variety of environmental conditions. The insilico model may also be used to interpret dynamic behaviors observed incell cultures (Covert M. W., Palsson B. O., J Biol Chem 277:28058-64(2002)).

When integrated as mentioned above, the regulatory/metabolic modelsrepresent a first-pass reconstruction and may be used for the generationof testable hypotheses (see FIG. 16). First, a phenotypic or behavioralshift of interest must be specified for a particular organism (e.g.,glucose-lactose diauxie in E. coli), as well as important regulatorygenes. The regulatory/metabolic model may then be used to simulatebehavior of the wild type strain over the course of the shift, as wellas behavior of knockout and/or mutant strains of the relevant regulatorygenes. These simulations represent hypotheses about the growth behavior,substrate uptake, by-product secretion, and gene expression over thecourse of the shift for each strain.

Strains of the organism are then obtained and/or constructed to build afull complement of the wild type as well as all corresponding knockoutstrains. Each strain is then cultured to monitor experimentally theshift in question. Rates of growth, uptake and secretion as well as geneexpression are monitored over the course of the shift using practicesthat are well known in the art (Ideker T., Thorsson V., Ranish J. A.,Christmas R., Buhler J., Eng J. K., Bumgarner R., Goodlett D. R.,Aebersold R., Hood L. Science 294:929-34 (2001)).

Once the necessary experimental data has been obtained, the experimentaloutcomes are compared rigorously to the computationally-generated data.This comparison will lead to (1) validation of certain regulatoryrelationships described by the model; (2) the identification ofregulatory relationships included in the model but for which theexperimental results were contradictory; and (3) the identification ofregulatory relationships which were not previously known which must beincorporated into the model. Both (2) and (3) represent areas where themodel may be improved.

Many genes are regulated by more than one transcription factor incertain organisms. Such genes correspond to complex Boolean logic rules,which must obtained by further experimentation. Specifically, for geneswhich are shown by the process above to be regulated by more than onetranscription factor, the multiple knockout strains may be constructed,in which to determine complex interactions. If two transcription factorsare required to affect the regulation of a gene, they have an ANDrelationship; if only one factor is required they have an ORrelationship.

The method is applied to the study of anaerobiosis in E. coli (FIG. 16).A large-scale model of metabolism and transcriptional regulation wasgenerated for E. coli previously (Covert M W, Palsson B O, J Bial Chem277:28058-64 (2002)). This model will be built up to the genome-scale(currently in progress) and used to generate predictions about growth,uptake and secretion rates as well as gene expression of E. coli underconditions of aerobic and anaerobic growth in glucose minimal media. Sixstrains—the appy, soxS, oxyR, fnr and arcA knockout strains as well asthe wild type—will be grown in batch culture as described above, withgrowth, uptake and secretion monitored continually. A sample will betaken at mid-log phase from which the mRNA will be extracted andanalyzed using Affymetrix Gene Chip technology. From this data, themodel will be evaluated both in terms of regulation (e.g., its abilityto predict gene induction/repression) and metabolism (e.g., its abilityto predict growth behavior of the wild type and mutant strains). Thisinformation will then be used to iteratively improve the model in termsof anaerobiosis prediction.

All journal article, reference and patent citations provided above, inparentheses or otherwise, whether previously stated or not, areincorporated herein by reference in their entirety.

Although the invention has been described with reference to the examplesprovided above, it should be understood that various modifications canbe made without departing from the spirit of the invention.

Example VI Iterative Refinement of a Regulatory Network Model Via aSystematic Model Improvement Algorithm

The purpose of this example is to illustrate the importance of thesystematic approach described above and depicted in FIG. 2 b to convergequickly on the best model of a biological process. Although ahypothetical regulatory network is used here as an example, this processis equally applicable to metabolic networks, signaling pathways, proteininteraction networks and any other biological processes.

A skeleton network of core metabolism was formulated earlier (Covert MW, Schilling C H, Palsson B. J Theor Biol. 213:73-88 (2001)). Itincludes 20 reactions, 7 of which are governed by regulatory logic. Thisnetwork is a highly simplified representation of core metabolicprocesses (e.g., glycolysis, the pentose phosphate pathway, TCA cycle,fermentation pathways, amino acid biosynthesis and cell growth), alongwith corresponding regulation (e.g., catabolite repression,aerobic/anaerobic regulation, amino acid biosynthesis regulation andcarbon storage regulation). A schematic of this skeleton network isshown in FIG. 18, together with a table containing all of the relevantchemical reactions and regulatory rules which govern the transcriptionalregulation. In terms of FIG. 2 b, this network will be considered theactual experimental system which is to be characterized.

To the right of the experimental system in FIG. 18 is the model of theexperimental system. The model is fairly complete, with one exception:the regulation of R5a in the model has not been correctly characterized,with no regulatory rule given (i.e., the reaction is expressed under allconditions).

A statement of scope and accuracy is determined for the model; namely,that the model will model the entire transcriptional regulatorycomponent of the system qualitatively, using Boolean logic, where a “1”indicates that the gene corresponding to a given reaction has beenexpressed and a “0” indicates that the gene has been down-regulated. Theexperiments of interest are growth of the system on metabolite Carbon2under aerobic and anaerobic conditions. For this example, the criterionfor the desired accuracy of the model is that the model error,calculated as the sum of the squared difference between the observed andpredicted expression of all regulated genes in the system, is equal tozero.

In Phase I of the process, an experiment is run with Carbon2 and Oxygenavailable to the system. The expression of the regulated genes in theexperimental and model system are calculated and shown in FIG. 19. Themodel error is equal to zero in this case, indicating that theexperimental data and the model predictions agree completely in thiscase.

Next, an experiment is run with Carbon2, but not Oxygen, available tothe system. In this case, there is a discrepancy between the observedand calculated expression of T5a, resulting in an error of one. Becausethe model error is greater than allowed by the stated criterion, aprocedure is implemented to alter the composition of the mathematicalmodel in such a way that the model error is minimized under the givenexperimental conditions. The procedure used in this case is developedwith the following assumption: the regulation of T5a depends on only oneof the known regulatory proteins (RPc1, RPb, RPh, and RPO2) in thesystem. The procedure is therefore as follows: (1) Obtain the activityof each protein as predicted by the model, (2) for each protein,generate a rule based on the activity of the given protein which resultsin the correct expression value for T5a, (3) recalculate the overallexpression array for the regulated genes, (4) evaluate the differencebetween the criterion for model accuracy by determining the new modelerror, and (5) choose the model(s) with the lowest error as the newmodel for future iterations.

The activity of the regulatory proteins under the given conditions are:RPc1=0, RPb=0, RPh=1, RPO2=1. For T5a to have a value of zero, the ruleswhich could be implemented are therefore: T5a=IF (RPc1), T5a=IF (RPb),T5a=IF NOT (RPh), and T5a=IF NOT (RPO2). The error of the model iscalculated with each new rule; and the new models all have an error ofzero, as shown in FIG. 19 (Phase III). As a result, one of the models(with new rule T5a=IF (RPc1), for example) is picked arbitrarily and theother equivalent solutions are stored.

The new model may then be reevaluated with data in the Phenotypicdatabase. For this example, data from the experiment where Carbon2 andOxygen were available to the system is compared to the predictions ofthe new model. The new model has an error with respect to theseconditions (shown in Phase IV of FIG. 19); as the other alternativesolutions are considered, only the model with new rule T5a=IF NOT (RPO2)fits the data with zero error. This model is kept for future iterations.

The process suggests a new experiment to further characterize theregulatory network: specifically, creating a RPO2 knockout strain of thesystem and testing the ability of the knockout strain to grow whereCarbon2 is available but Oxygen is not. As shown in FIG. 19, the modelpredictions and experimental data are also in agreement for thisexperiment.

The model has therefore been used to drive an experimental process wherenew data has been generated to improve model predictions and bettercharacterize the experimental system itself, as well to suggest a newround of experiments which can be performed to gain further knowledgeand insight.

Example VII Decomposing Steady State Flux Distributions into ExtremePathways Using the Alpha-Cone Method

This example shows how an arbitrary steady state phenomenological fluxdistribution can be decomposed in a principled fashion into systemicpathways (here extreme pathways) to identify operational pathways in abiosystem. The alpha-cone decomposition method allows identifying therange of systemic pathway weightings for a given flux distribution aswell as defining the minimal set of systemic pathways required todescribe a phenomenological pathway. This minimal set of systemicpathways together with the range of possible weightings of thesepathways defines the operational pathways of the biosystem.

The sample metabolic network used for this analysis has been publishedpreviously (Covert M. W., Schilling C. H., Palsson B. J Theor Biol213:73-88 (2001)). The network consists of 20 reactions and 16 internalmetabolites. The example network was designed to mirror some of the coremetabolic processes such as glycolysis, the citric acid cycle, andrespiration. The extreme pathways of this network were calculatedpreviously (Covert M W & Palsson B O. J Theor Biol 216 (2003)). Thenetwork has 80 Type I extreme pathways that are included in thisanalysis. Each extreme pathway, pi, was scaled to its maximum possibleflux based on the maximum value of the uptake reactions (V_(max)). Amatrix P is then formed using p_(i) (i=1 . . . n, where n is the numberof extreme pathways for the system) as its columns.

To mimic phenomenological flux distributions produced by experimentalmeasurements the steady state flux distributions for this network werecalculated using the well-established technique of flux balance analysis(FBA). For the purposes of this study, unique steady state fluxdistributions were calculated for various environmental conditions.

For a given phenomenological flux distribution the decompositionweightings on the extreme pathways (denoted by α) are not usuallyunique. The rank of the P matrix determines the number of consistentequations and is usually smaller than the number of extreme pathways,resulting in extra degrees of freedom. This results in an “alpha space”of allowable extreme pathway weightings. In order to elucidate the rangeof possible alpha values that could contribute to the steady statesolution, the alpha-spectrum was developed based on the equation P.α=vwhere P is a matrix of extreme pathway vectors (extreme pathways are thecolumns, reactions are the rows), α is a vector of alpha weightings onthe pathways and v an arbitrary steady state flux distribution that isto be decomposed. For each individual extreme pathway defined for thenetwork, the alpha weighting for that pathway was both maximized andminimized using linar programming while leaving all other extremepathway alpha weightings free. This resulted in an allowable alpha rangefor each extreme pathway. The results were then plotted on a2-dimensional graph with the extreme pathways on the x-axis and therange of alpha weightings on the y-axis. Since the pathways arenormalized to V_(max), the alpha weightings correspond to a percentageusage of each extreme pathway. Some extreme pathways are not used whileothers can have a range of alpha weightings.

In addition to defining the alpha-spectrum, mixed integer linearprogramming (MILP) (Williams, H P Model building in mathematicalprogramming. Chichester; New York, Wiley (1990)) was used to find theminimum number of extreme pathways that were needed to describe a givenphenomenological flux distribution in cases where multiple pathwaycombinations exist. The usage of a specific extreme pathway wasrepresented by a Boolean variable (β_(j) which was assumed to have avalue of 1 when the corresponding pathway is used and zero when thepathway is not used. The sum of all Boolean variables representingpathway usage was minimized to obtain the alpha weightings correspondingto the case where the least number of pathways was used. Thecorresponding optimization problem can be formally described as:

${Min}{\sum\limits_{i = 1}^{n_{p}}\; \beta_{i}}$ P α = v0 ≤ α_(i) ≤ β_(i)

where β is the vector of the Boolean variables corresponding to thepathway usage and a is the vector of the pathway weightings. Thesolution is a set of alpha weightings such that the minimum number ofextreme pathways are used to obtain the decomposition of the desiredphenomenological flux distribution.

The methods described above were applied to the case of aerobic growthwith no regulation included. This case was essentially unrestricted asall possible substrates (Carbon 1, Carbon 2, F, H, and Oxygen) wereprovided to the network. The resulting flux distribution computed usingFBA can be seen in FIG. 20A. The calculated alpha-spectrum shows that ofthe 80 Type I pathways, only 13 could be used in reconstructing theaerobic flux distribution (FIG. 20B). Pathway 52 can range from 0 to 1(0 to 100% of its maximum possible usage). Pathway 36 must be used asindicated by the non-zero minimum alpha value. The remaining 11 pathwaysvary from 0 to various sub-maximum values. An MILP analysis was done todetermine the minimum number of pathways needed to produce the aerobicsteady state flux distribution. When the MILP was solved withoutadditional constraints, P36 was used to its maximum capacity (100%) withsub-maximal contributions from pathways 48, 38, 66, and 8.Interestingly, when the network was forced to maximally use the pathwaywith the greatest alpha range (P52), pathway 36 was also used, albeitsub-maximally, along with pathways 12, 32, and 60. Note that with theexception of P36, which has a non-zero minimum possible weighting andthus has to be used in all possible solutions, there are no pathways incommon between the two sets of MILP solutions (FIG. 20C).

While the alpha-cone method was demonstrated above for a fluxdistribution obtained through an FBA calculation, it is be possible touse experimentally determined metabolic flux data in the analysis aswell. Even given partial or fragmented flux data, it will be possible todetermine the candidate alpha-spectrum and hence obtain the operationalpathways active in a cell in a given external condition.

TABLE 1 Reaction/Gene Enzyme Name Reaction Membrane TransportPhosphotransferase system pts GLCxt + PEP→ G6P + PYR Succinate transportSUCC trx SUCCxt

 SUCC Acetate transport AC trx ACxt

 AC Ethanol transport ETH trx ETHxt

 ETH Oxygen transport O2 trx O2xt

 O2 Carbon dioxide transport CO2 trx CO2xt

 CO2 Phosphate transport Pi trx PIxt

 PI Glycolysis Phosphoglucose isomerase pgi G6P

 F6P Phosphofructokinase pfkA F6P + ATP→ FDP + ADPFructose-1,6-bisphosphatase fbp FDP → F6P + PIFructose-1,6-bisphosphatate aldolase fba FDP

 T3P1 + T3P2 Triosphosphate Isomerase tpiA T3P2

 T3P1 Glyceraldehyde-3-phosphate dehydrogenase gapA T3P1 + PI + NAD

 NADH + 13PDG Phosphoglycerate kinase pgk 13PDG + ADP

 3PG + ATP Phosphoglycerate mutase 1 gpmA 3PG

 2PG Enolase eno 2PG

 PEP Pyruvate Kinase II pykA PEP + ADP→ PYR + ATP Phosphoenolpyruvatesynthase ppsA PYR + ATP→ PEP + AMP + PI Pyruvate dehydrogenase aceEPYR + COA + NAD→ NADH + CO2 + ACCOA Pentose Phosphate Shunt Glucose6-phosphate-1-dehydrogenase zwf G6P + NADP

 D6PGL + NADPH 6-Phosphogluconolactonase pgl D6PGL→ D6PGC6-Phosphogluconate dehydrogenase gnd D6PGC + NADP

 NADPH + CO2 + RL5P Ribose-5-phosphate isomerase A rpiA RL5P

 R5P Ribulose phosphate 3-epimerase rpe RL5P

 X5P Transketolase I tldA1 R5P + X5P

 T3P1 + S7P Transaldolase B talA T3P1 + S7P

 E4P + F6P Transketolase II tktA2 X5P + E4P

 F6P + T3P1 TCA cycle Citrate synthase gltA ACCOA + OA→ COA + CITAconitase A acnA CIT

 ICIT Isocitrate dehydrogenase icdA ICIT + NADP

 CO2 + NADPH + AKG 2-Ketoglutarate dehyrogenase sucA AKG + NAD + COA→CO2 + NADH + SUCCOA Succinyl-CoA synthetase sucC SUCCOA + ADP + PI

 ATP + COA + SUCC Succinate dehydrogenase sdhA1 SUCC + FAD→ FADH + FUMFumurate reductase frdA FUM + FADH→ SUCC + FAD Fumarase A fumA FUM

 MAL Malate dehydrogenase mdh MAL + NAD

 NAPH + OA Dissimttation of Pyruvate Acetaldehyde dehydrogenase adhEACCOA + 2 NADH→ ETH + 2 NAD + COA Phosphotransacetylase pta ACCOA + PI

 ACTP + COA Acetate kinase A ackA ACTP + ADP

 ATP + AC Anapleurotic Reactions Phosphoenolpyruvate carboxykinase pckAOA + ATP→ PEP + CO2 + ADP Phosphoenolpyruvate carboxylase ppc PEP + CO2→OA + PI Energy/Redox Metabolism NADH dehydrogenase I nuoA NADH + Q→NAD + QH2 + 2 HEXT Cytochrome oxidase bo3 cyoA QH2 + ½ O2→ Q + 2 HEXTPyridine nucleotide transhydrogenase pntA NADPH + NAD→ NADP + NADHSuccinate dehydrogenase complex sdhA2 FADH + Q→ FAD + QH2 F0F1-ATPaseatpABCDEFGHI ADP + PI + 3 HEXT→ ATP Adenylate kinase adk ATP + AMP

 2 ADP ATP drain ATP dr ATP → ADP + PI Growth Flux Growth flux GRO 41.3ATP + 3.5 NAD + 18.2 NADPH + 0.2 G6P + 0.1 F6P + 0.9 R5P + 0.4 E4P + 0.1T3P1 + 1.5 3PG + 0.5 PEP + 2.8 PYR + 3.7 ACCOA + 1.8 OA + 1.1 AKG→ 41.3ADP + 41.3 PI + 3.5 NADH + 18.2 NADP + 3.7 COA + 1.0 BIOMASS ExchangeFluxes Glucose external GLCxt GLCxt→ Succinate external SUCCxt SUCCxt→Ethanol external ETHxt ETHxt→ Acetate external ACxt ACxt→ Biomass drainBIOMASS BIOMASS→ Phosphate external PIxt PIxt→ Carbon dioxide externalCO2xt CO2xt→ Oxygen external O2xt O2xt→

TABLE 2 Exchange Fluxes Pathway SUCCxt/ ETHxt/ ACxt/ GRO/ PIxt/ CO2xt/O2xt/ Number SUCCxt SUCCxt SUCCxt SUCCxt SUCCxt SUCCxt SUCCxt NetPathway Reaction Balance 33 −1.000 0 0 0.051 −0.188 1.825 −1.267SUCCxt + 0.188 PIxt + 1.267 O2xt ---> 0.051 GRO + 1.825 CO2xt 30 −1.0000 0 0.034 −0.125 2.553 −2.014 SUCCxt + 0.125 PIxt + 2.014 O2xt --->0.034 GRO + 2.553 CO2xt 32 −1.000 0 0 0.033 −0.121 2.600 −2.062 SUCCxt +0.121 PIxt + 2.062 O2xt ---> 0.033 GRO + 2.6 CO2xt 34 −1.000 0 0 0.049−0.182 1.895 −1.338 SUCCxt + 0.182 PIxt + 1.338 O2xt ---> 0.049 GRO +1.895 CO2xt 22 −1.000 0 0 0.032 −0.117 2.644 −2.108 SUCCxt + 0.117PIxt + 2.108 O2xt ---> 0.032 GRO + 2.644 CO2xt 14 −1.000 0 0 0.031−0.114 2.679 −2.144 SUCCxt + 0.114 PIxt + 2.144 O2xt ---> 0.031 GRO +2.679 CO2xt 18 −1.000 0.549 0 0.025 −0.092 1.837 −0.759 SUCCxt + 0.092PIxt + 0.759 O2xt ---> 0.025 GRO + 1.837 CO2xt + 0.549 ETHxt 31 −1.000 00.158 0.047 −0.172 1.696 −1.142 SUCCxt + 0.172 PIxt + 1.142 O2xt --->0.047 GRO + 1.696 CO2xt + 0.158 ACxt 10 −1.000 0 0 0 0 4.000 −3.500SUCCxt + 3.5 O2xt ---> 4.0 CO2xt 5 −1.000 0 1.000 0 0 2.000 −1.500SUCCxt + 1.5 O2xt ---> 2.0 CO2xt + 1.0 ACxt 2 −1.000 1.000 0 0 0 2.000−0.500 SUCCxt + 0.5 O2xt ---> 2.0 CO2xt + 1.0 ETHxt 26 −1.000 0 0 0 04.000 −3.500 SUCCxt + 3.5 O2xt ---> 4.0 CO2xt

TABLE 3 Angles Path- Diff Path- Net Path- (degree) way # Fluxes (%) way# Diff (%) way # 4.62E−05 P_33 0 P_33 5.84E−05 P_33 4.9 P_32 3.5 P_3411.3 P_32 11.1 P_30 5.3 P_22 22.4 P_30 22.6 P_31 5.3 P_30 36.8 P_31 25.2P_34 8.8 P_14 67.1 P_2 26.1 P_22 8.8 P_31 67.8 P_34 27.0 P_14 10.5 P_3270.7 P_5 27.7 P_18 14.0 P_18 72.2 P_22 38.8 P_10 22.8 P_26 76.3 P_1440.1 P_5 38.6 P_10 79.6 P_18 40.4 P_26 52.6 P_2 177.0 P_10 41.5 P_2 52.6P_5 233.1 P_26

TABLE 4 Angles Path- Diff Path- Net Path- (degree) way # Fluxes (%) way# Diff (%) way # 2.3 P_32 3.5 P_32 5.2 P_32 2.6 P_33 7.0 P_33 6.4 P_3310.9 P_30 10.5 P_34 25.1 P_30 21.9 P_31 12.3 P_22 35.8 P_31 25.9 P_3412.3 P_30 66.9 P_2 26.9 P_22 15.8 P_14 71.4 P_5 27.8 P_14 15.8 P_31 75.3P_34 28.4 P_18 21.1 P_18 79.9 P_22 39.5 P_10 29.8 P_26 84.1 P_14 39.5P_5 45.6 P_10 87.5 P_18 40.5 P_26 45.6 P_5 187.6 P_10 41.0 P_2 59.6 P_2241.7 P_26

TABLE 5 Nucleotide Amino Acid Variant Type Change Change Result B+normal none none A+ non-chronic  376 A→G Asn→Asp polar to acidic A−non-chronic  376 A→G Asn→Asp polar to acidic  202* G→A Val→Met nonpolarto nonpolar Mediterranean non-chronic  563 C→T Ser→Phe polar to nonpolarTsukui chronic 561-563 del 188/189 del Minnesota chronic  637 G→T 213Val → Leu nonpolar to nonpolar Asahikawa chronic  695 G→A 232 Cys→Tyrslightly polar to nonpolar Durham chronic  713 A→G 238 Lys→Arg basic tobasic Wayne chronic  769 C→G 257 Arg→Gly basic to nonpolar Loma Lindachronic 1089 C→A 363 Asn→Lys polar to basic Tomah chronic 1153 T→C 385Cys→Arg slightly polar to basic Iowa chronic 1156 A→G 386 Lys→Glu basicto acidic Walter Reed chronic 1156 A→G 386 Lys→Glu basic to acidic IowaCity chronic 1156 A→G 386 Lys→Glu basic to acidic Springfield chronic1156 A→G 386 Lys→Glu basic to acidic Guadalajara chronic 1159 C→T 387Arg→Cys basic to slightly polar Iwate chronic 1160 G→A 387 Arg→His basicto acidic/basic Niigata chronic 1160 G→A 387 Arg→His basic toacidic/basic Yamaguchi chronic 1160 G→A 387 Arg→His basic toacidic/basic Portici chronic 1178 G→A 393 Arg→His basic to acidic/basicAlhambra chronic 1180 G→C 394 Val→Leu nonpolar to nonpolar Tokyo chronic1246 G→A 416 Glu→Lys acidic to basic Fukushima chronic 1246 G→A 416Glu→Lys acidic to basic Atlanta chronic 1284 C→A 428 Tyr→End Pawneechronic 1316 G→C 439 Arg→Pro basic to nonpolar Morioka chronic 1339 G→A447 Gly→Arg nonpolar to basic

TABLE 6 Nucleotide Amino Acid Variant Change Change Result Sassari  514G→C Glu→Gln acidic to slightly polar Parma not characterized — — 1456C→T Arg→Trp basic to nonpolar Soresina 1456 C→T Arg→Trp basic tononpolar 1552 C→A Arg→Ser basic to slightly polar Milano 1456 C→TArg→Trp basic to nonpolar Brescia 1042-1044 del Lys deleted basicdeleted 1456 C→T Arg→Trp basic to nonpolar Manatova 1168 G→A Asp→Asnacidic to slightly polar

1. A method of diagnosing a genetic polymorphism-mediated pathology,comprising: (a) applying a biochemical or physiological conditionstressing a physiological state of a reaction network representing abiosystem with a genetic polymorphism-mediated pathology, said appliedbiochemical or physiological condition correlating with said geneticpolymorphism-mediated pathology; and (b) measuring one or morebiochemical or physiological indicators of said pathology within saidreaction network, wherein a change in said one or more biochemical orphysiological indicators in said stressed state compared to anunstressed physiological state indicates the presence of a geneticpolymorphism corresponding to said pathology.
 2. The method of claim 1,wherein said biochemical or physiological condition is selected from achange in flux load, pH, reactants, and products.
 3. The method of claim1, wherein said biochemical or physiological condition comprises anoxidative load or an energy load.